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2015 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
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Table of Contents
Organization…………………………………………………………………………………………………………………………..2
Objectives……………………………………………………………………………………………………………………………...2
Organizing Committee………..……………………………………………………….…………………………………………..2
Conference Homepage……………………………………………………………………………………………….......... 2
Sponsors………………………………………………………………………………………………………………………...........2
Useful Information……………………………………………………………………………………………………………...3
Venue…………………………………………………………………………………………………………………………………….3
Registration…………….……………………………………………………………………………………………………………….3
Hotel……………………………………………………………………………………………………………………………………….3
Transportation Directions……………………………………………………………………………………………………….3
Internet Access…………………………………………………………………………………………………………………..5
Useful Links……………………………………………………………………………………………………………………………...5
Emergency Contact………………………………………………………………………………………………………………….5
List of Participants…………………………………………………………………………………………………………………6
PDE Graduate Students at SJTU…………………………………………………………………………………………12
Talk Schedule…………………………………………………………………………………………………………………………13
Schedule by Day………………….……………….……..…………………………………………..………………………….13
Abstracts………………………………………………………………………………………………………………………………13
2015 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
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Objectives
The purpose of this conference is to bring together mathematicians from all over the world
in the area of Nonlinear Evolutionary Partial Differential Equations to present their recent
research results, to exchange new ideas and to discuss current challenging issues. The
main topics include:
Hyperbolic Problems
Parabolic and Elliptic Equations
Equations of Mixed Type
Conservation Laws
Euler Equations and Navier-Stokes Equations
Boltzmann Equation
Applications of PDEs
Organizing Committee
Alberto Bressan (The Penn State University, USA)
Gui-Qiang Chen (University of Oxford, UK)
Mikhail Feldman (University of Wisconsin-Madison, USA)
Yachun Li (co-chair, Shanghai Jiao Tong University, China)
Chun Liu (The Penn State University, USA)
Yuejun Peng (Université Blaise Pascal, France)
Weike Wang (Shanghai Jiao Tong University, China)
Ya-Guang Wang (co-chair, Shanghai Jiao Tong University, China)
Endre Suli (University of Oxford, UK)
Tong Yang (City University of Hong Kong, China)
Conference Homepage
http://math.sjtu.edu.cn/conference/2015NEPDE/Default.aspx
Sponsors
The organizing committee wishes to extend their thanks and appreciation to the sponsors
for their generous support:
◎ Department of Mathematics, Shanghai Jiao Tong University
◎ The Zhiyuan Center for Mathematical Sciences (supported by The National Natural
Science Foundation of China), Shanghai Jiao Tong University
2015 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
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Useful Information
Venue
June 2-7
Lecture Hall (100-L), Math Building, SJTU
Address: No. 800, Dongchuan Road, Minhang District, Shanghai, China
(上海交通大学闵行校区地址：上海市闵行区东川路 800 号)
Registration
The registration will be held from 14:00 to 20:00, June 1，Academic Exchange Center lobby
(学术活动中心大厅), Shanghai Jiao Tong University. We will also set tables every day at
the lobby of Math Building, SJTU.
Hotel
Academic Exchange Center (学术活动中心)
Minhang Campus, SJTU
800 Dongchuan Rd. Minhang District, Shanghai 200240, China
Tel: 86-21-54740800
Check-in
We have reserved a hotel room for you in your name so that you can directly check in at
the reception once you arrive.
Meals
◎ Breakfast: Hotel rate has already included breakfast. The breakfast will be available
from 7:00am-9:30am.
◎ Lunch: Marco Polo Buffet (June 2, 3, 4, 5)；Academic Exchange Center 2/F (June 6, 7)
◎ Dinner: Liu Yuan (June 2, 3, 4, 5，6，7 )
Transportation Directions
From Pudong International Airport (PVG) to the Academic Exchange Center, SJTU
Please give the following message to the taxi driver if you don’t speak Chinese:
请送我到闵行区东川路800号上海交通大学学术活动中心。
请走S32（从1号航站楼上S32）到剑川路下，到红绿灯处往右拐上剑川路，左拐至沧源路，
再左拐至东川路，进东川路 800 号（近永平路）大门进，进门后往右行驶50米即可见学术
活动中心。
2015 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
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Please take me to Academic Center of Shanghai Jiao Tong University, located at 800
Dongchuan Road Minhang District
Please take highway S32 (from Terminal 1), exit on Jianchuan Road. Right turn at the
traffic lights to Jianchuan Road, then turn left to Cangyuan Road, followed by left turn to
Dongchuan Road. 800 Dongchuan Road (the gate of SJTU at the cross of Dongchuan
Road and Yongping Road) is on your left, Enter the gate, turn right and the Academic
Center is about 50 meters on your right.
From Hongqiao Airport (SHA) to the Academic Exchange Center, SJTU
Please give the following message to the taxi driver if you don’t speak Chinese:
请送我到闵行区东川路800号上海交通大学学术活动中心。
请走S4高架到剑川路下，到红绿灯处往右拐上剑川路，左拐至沧源路，再左拐至东川路，进
东川路 800 号（近永平路）大门进，进门后往右，学术活动中心在50米后右手边。
Please take me to Academic Center of Shanghai Jiao Tong University, located at 800
Dongchuan Road Minhang District
Please take highway S4, exit on Jianchuan Road. Right turn at the traffic lights to
Jianchuan Road, then turn left to Cangyuan Road, followed by left turn to Dongchuan Road.
800 Dongchuan Road is on your left which is the gate of SJTU. Enter the gate, turn right
and the Academic Center is about 50 meters on your right.
From Pudong International Airport (PVG) to the Department of Mathematics, SJTU
Please give the following message to the taxi driver if you don’t speak Chinese:
请送我到闵行区东川路800号上海交通大学数学楼。
请走S32（从1号航站楼上S32）到剑川路下，到红绿灯处往右拐上剑川路，左拐至沧源
路，再左拐至东川路，进东川路 800 号（近永平路）大门进，进门后向左，然后向北直
行200米即可见数学楼。
Please take me to the Department of Mathematics, Shanghai Jiao Tong University, located
at 800 Dongchuan Road Minhang District
Please take highway S32 (from Terminal 1), exit on Jianchuan Road. Right turn at the
traffic lights to Jianchuan Road, then turn left to Cangyuan Road, followed by left turn to
Dongchuan Road. 800 Dongchuan Road (the gate of SJTU at the cross of Dongchuan
Road and Yongping Road) is on your left, turn left and go straight toward north and the
Department of Mathematics is about 200 meters on your right.
From Hongqiao International Airport (SHA) to the Department of Mathematics, SJTU
Please give the following message to the taxi driver if you don’t speak Chinese:
请送我到闵行区东川路800号上海交通大学数学楼。
请走S4到剑川路下，到红绿灯处往右拐上剑川路，沿剑川路向西，左拐至沧源路，再左拐
至东川路，进东川路 800号（近永平路）大门进，进门后向左，然后向北直行200米即可
见数学楼。
Please take me to the Department of Mathematics, Shanghai Jiao Tong University, located
at 800 Dongchuan Road，Minhang District
Please take highway S4, exit on Jianchuan Road. Right turn at the traffic lights to
Jianchuan Road, then turn left to Cangyuan Road, followed by left turn to Dongchuan Road.
2015 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
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800 Dongchuan Road (the gate of SJTU at the cross of Dongchuan Road and Yongping
Road) is on your left, turn left and go straight toward north and the Department of
Mathematics is about 200 meters on your right.
Please ask the driver call 13918684080 (cell of Limin Qin) for emergency.
Chinese: 司机，如有问题请打秦丽敏手机：13918684080
Internet Access
Wireless internet access is available in the Lecture Hall (100-M).
The user name is mathconference and the password is: 12345678
Useful Links
Shanghai Jiao Tong University: www.sjtu.edu.cn
Department of Mathematics, SJTU: www.math.sjtu.edu.cn
Conference Webpage: http://math.sjtu.edu.cn/conference/2015NEPDE/Default.aspx
Emergency Contact
Contact: Limin Qin (Cell: 13918684080)
Huiyu Zhu (Cell: 13917204456)
2015 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
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List of Participants
1. Myoungjean Bae (Pohang University of Science and Technology, Korea)
2. Yu-e Bao (Inner Mongolia University for Nationalities, China)
3. Alberto Bressan (The Penn State University, USA)
4. Tristan Buckmaster (New York University, USA)
5. Jionghui Cai (Yuxi Nomal University, China)
6. Jun Cao (Yuxi Nomal University, China)
7. Gilles Carbou (Université de Pau et des Pays de l'Adour, France)
8. Jianjun Chen (Shanghai University, China)
9. Shuxing Chen (Fudan University, China)
10. Tingting Chen (Wuhan institute of physics and mathematics，CAS, China)
11. Andrea Corli (University of Ferrara, Italy)
12. Bo-Qing Deng (Anhui University, China)
13. Shijin Deng (Shanghai Jiao Tong University, China)
14. Qiang Du (The Penn State University, USA)
15. Qin Duan (Shen Zhen University, China)
16. Renjun Duan (The Chinese University of Hong Kong, China)
17. Lili Fan (Wuhan Polytechnic University, China)
18. Beixiang Fang (Shanghai Jiao Tong University, China)
19. Eduard Feireisl (The Academy of Sciences of Czech Republic, Czech Republic)
20. Hermano Frid (Instituto de Matemática Pura e Applicada-IMPA, Brazil)
21. Bin Ge (Harbin Engineering University, China)
22. Huajun Gong (Shenzhen University ,China)
2015 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
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23. Qilong Gu (Shanghai Jiao Tong University, China)
guql @sjtu.edu.cn
24. Pigong Han (Academy of Mathematics and Systems Science，CAS, China)
25. Kai Hu (Southwest University, China)
26. Xianpeng Hu (City University of Hong Kong, China)
27. Weifeng Jiang (Wuhan Institute of Physics and Mathematics，CAS, China)
28. Shi Jin (Shanghai Jiao Tong University, China)
29. Yoshiyuki Kagei (Kyushu University, Japan)
30. Shuichi Kawashima (Kyushu University, Japan)
31. Geng Lai (Shanghai University, China)
32. Mijia Lai (Shanghai Jiao Tong University, China)
33. Zhen Lei (Fudan University, China)
34. Congming Li (Shanghai Jiao Tong University, China)
35. Daqian Li (Chinese Academy of Sciences, China)
36. Dening Li (West Virginia University, USA)
37. Hailiang Li (Capital Normal University, China)
38. Gang Li (Huazhong Univercity of Science and Technology, China)
39. Jiequan Li (Beijing Normal University, China)
40. Tong Li (University of Iowa, USA)
41. Yachun Li (Shanghai Jiao Tong University, China)
42. Yi Li (Shanghai Jiao Tong University, China)
43. Ze Li (University of Science and Technology of China, China)
44. Naian Liao (Chongqing University, China)
45. Chun Liu (The Penn State University, USA)
2015 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
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46. Jianli Liu (Shanghai University, China)
47. Shannian Lu (Columbia University and Penn State University, USA)
48. Zhaoyang Liu (Shanghai University, China)
49. Tao Luo (Georgetown University, USA)
50. Xiuwen Luo (Fudan University, China)
51. Shixiang Ma (South China Normal University, China)
52. Stefano Modena (SISSA, Italy)
53. Shankar Rao Munjam (Pondicherry University-Pondicherry, India)
54. Vincent Munnier (Shanghai Jiao Tong University, China)
55. Cunyun Nie (Hunan Institute of Engineering, China)
56. Ronghua Pan (Georgia Institute of Technology, USA)
57. Congming Peng (Lanzhou University, China)
58. Yue-Jun Peng (Université Blaise Pascal, France)
59. Yuming Qin (Donghua University, China)
60. Aifang Qu (Wuhan Institute of Physics and Mathematics，CAS, China)
61. Reinhard Racke (University of Konstanz, Germany)
62. Paolo Secchi (University of Brescia, Italy)
63. Shaoqiang Shang (The Northeast Forestry University, China)
64. Wen Shen (The Penn State University, USA)
65. Wancheng Sheng (Shanghai University, China)
66. Marshall Slemrod (University of Wisconsin at Madison, USA)
67. Ming Song (Shaoxing University，China)
2015 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
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68. Yuhua Sun (Nankai University，China)
69. Youshan Tao (Donghua University, China)
70. Kaimin Teng (Taiyuan University of Technology, China)
71. Shouke Tian (Shanghai University, China)
72. Athanasios Tzavaras (King Abdullah University of Science and Technology, Saudi
Arabia)
73. Alexis F. Vasseur (University of Texas at Austin, USA)
74. Chunpeng Wang (Jilin University, China)
75. Dehua Wang (University of Pittsburgh, USA)
76. Fang Wang (Shanghai Jiao Tong University, China)
77. Hongwei Wang (Anyang Normal University, China)
78. Kai Wang (Lanzhou University, China)
79. Lihe Wang (Shanghai Jiao Tong University, China)
80. Liangchen Wang (Chongqing University, China)
81. Qingxuan Wang (Lanzhou University，China)
82. Shu Wang (Beijing University of Technology, China)
83. Weike Wang (Shanghai Jiao Tong University, China)
84. Xiao-Ping Wang (Hong Kong University of Science and Technology, China)
85. Ya-Guang Wang (Shanghai Jiao Tong University, China)
86. Yun Wang (Soochow University, China)
87. Yuzhu Wang (North China University of Water Resources and Electric Power, China)
88. Jinbo Wei (University of Science and Technology, China)
2015 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
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89. Shangkun Weng (Pohang University of Science and Technology, Korea)
90. Hao Wu (Fudan University, China)
91. Jiahong Wu (Oklahoma State University, USA)
92. Simo Wu (The Penn State University, USA)
93. Wei Xiang (City University of Hong Kong, China)
94. Qinghua Xiao (Wuhan Institute of Physics and Mathematics, CAS, China)
95. Chunjing Xie (Shanghai Jiao Tong University, China)
96. Feng Xie (Shanghai Jiao Tong University, China)
97. Deliang Xu (Shanghai Jiao Tong University, China)
98. Yongzhong Xu (Shanghai Jiao Tong University, China)
99. Kai Yan (Huazhong University of Science and Technology, China)
100. Deane Yang (New York University, USA)
101. Chenxi Yang (Yuxi Nomal University, China)
102. Kailong Yang (University of Science and Technology of China, China)
103. Meihua Yang (Huazhong University of Science and Technology, China)
104. Tong Yang (City University of Hong Kong, China)
105. Xiaozhou Yang (Wuhan Institute of Physics and Mathematics, CAS, China )
106. Xiongfeng Yang (Shanghai Jiao Tong University, China) [email protected]
107. Aidi Yao (Shanghai University, China)
108. Chao Yi (Fudan University, China)
109. Hui Yin (Huazhong University of Science and Technology, China)
110. Park Yong (Pohang University of Science and Technology, Korea)
2015 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
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111. Wen-An Yong (Tsinghua University, China)
112. Hongjun Yu (South China Normal University, China)
113. Hairong Yuan (East China Normal University, China)
114. Chongchun Zeng (Georgia Institute of Technology, USA)
115. Chao Zhang（Harbin Institute of Technology, China）
116. Jun-qing Zhang (Changzhi College, China)
117. Qidi Zhang（East China University of Science and Technology，China）
118. Qingling Zhang (Jianghan University, China)
119. Qinglong Zhang (Shanghai University, China)
120. Shuyi Zhang (Shanghai University of International Business and Economics, China)
121. Ting Zhang (Zhejiang University, China)
122. Wei Zhang (Yuxi Nomal University, China)
123. Zhipeng Zhang (Nanjing University, China)
124. Chunqin Zhou (Shanghai Jiao Tong University, China)
125. Fujun Zhou (South China University of Technology, China)
126. Yi Zhou (Fudan University, China)
127. Yong Zhou (Shanghai University of Finance and Economics, China)
128. Yi Zhu (Fudan University, China)
2015 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
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PDE Graduate Students at SJTU
1. Yue Cao (Shanghai Jiao Tong University, China)
2. Jiao Chen (Shanghai Jiao Tong University, China)
3. Hao Li (Shanghai Jiao Tong University, China)
4. Jianbo Li (Shanghai Jiao Tong University, China)
5. Guowei Liu (Shanghai Jiao Tong University, China)
6. Lei Ma (Shanghai Jiao Tong University, China)
7. Ruixuan Ma (Shanghai Jiao Tong University, China)
8. Zhaoyang Shang (Shanghai Jiao Tong University, China)
9. Renkun Shi (Shanghai Jiao Tong University, China)
10. Shuai Xi (Shanghai Jiao Tong University, China)
11. Xin Xu (Shanghai Jiao Tong University, China)
12. Rui Xue (Shanghai Jiao Tong University, China)
13. Kaifei Yao (Shanghai Jiao Tong University, China)
14. Siqi Yao (Shanghai Jiao Tong University, China)
15. Jierong Yin (Shanghai Jiao Tong University, China)
16. Liang Zhao (Shanghai Jiao Tong University, China)
17. Shengguo Zhu (Shanghai Jiao Tong University, China)
18. Shiyong Zhu (Shanghai Jiao Tong University, China)
NEPDE 2015 –Talk Schedule
Time June 2 (Tue.) June 3 (Wed.) June 4 (Thur.) June 5 (Fri.) June 6 (Sat.) June 7 (Sun.)
Mo
rnin
g S
essio
n
08:20-08:30 Opening
Chair Shuxing Chen Marshall Slemrod Shuichi Kawashima Hailiang Li Alexis F. Vasseur Hermano Frid
08:30-09:10 Alberto Bressan Shuichi Kawashima Eduard Feireisl Stefano Modena Tao Luo Wen-An Yong
09:10-09:50 Marshall Slemrod Paolo Secchi Alexis F. Vasseur Athanasios Tzavaras Chongchun Zeng Xiaozhou Yang
9:50-10:30 Xiao-Ping Wang Jiahong Wu Ronghua Pan Shu Wang Deane Yang Ting Zhang
20 min Tea Break
Chair Alberto Bressan Ya-Guang Wang Eduard Feireisl Athanasios Tzavaras Ronghua Pan Chun Liu
10:50-11:30 Qiang Du Reinhard Racke Dehua Wang Hailiang Li Gilles Carbou Chunjing Xie
11:30-12:10 Chun Liu Yoshiyuki Kagei Chunpeng Wang Yuming Qin Hongjun Yu Hao Wu
Lunch Break
Afte
rno
on
Se
ssio
n
Chair Congming Li Reinhard Racke Dehua Wang
Half-day Break
Qiang Du Tao Luo
14:00-14:40 Yi Zhou Andrea Corli Myoungjean Bae Jiequan Li Yong Zhou
14:40-15:20 Zhen Lei Wen Shen Wei Xiang Xianpeng Hu Tristan Buckmaster
20 min Tea Break 20 min Tea Break
Chair Andrea Corli Paolo Secchi Weike Wang Yue-Jun Peng Yachun Li
15:40-16:20 Dening Li Hermano Frid Wancheng Sheng Beixiang Fang Hairong Yuan
16:20-17:00 Aifang Qu Yue-Jun Peng Tong Li Qilong Gu Shuyi Zhang
17:00-17:40 Shangkun Weng Renjun Duan Youshan Tao Mijia Lai Vincent Munnier
18:00 Dinner
2015 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
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Schedule by Day
June 2 , Day 1: Lecture Hall, Department of Mathematics
Morning Session
08:20-08:30 Opening
Session 1 Chair: Shuxing Chen
08:30-09:10 Alberto Bressan
A Lipschitz Metric for the Flow of a Nonlinear Wave Equation
09:10-09:50 Marshall Slemrod
The Problem with Hilbert’s 6th Problem
09:50-10:30 Xiao-Ping Wang A One-domain Approach for Modeling and Simulation of Free Fluid over a Porous Medium
10:30-10:50 Tea Break
Session 2 Chair: Alberto Bressan
10:50-11:30 Qiang Du Nonlocal Balance Laws and Their Numerical Approximations
11:30-12:10 Chun Liu Energetic Variational Approaches for Transport of Charged Particles
12:10-14:00 Lunch Break
Afternoon Session
Session 1 Chair: Congming Li
14:00-14:40 Yi Zhou Vanishing Viscosity Method for Non-identity Viscosity Matrix
14:40-15:20 Zhen Lei Global WP of Incompressible Elastodynamics in 2D
15:20-15:40 Tea Break
Session 2 Chair: Andrea Corli
15:40-16:20 Dening Li Data Compatibility for 3-D Euler Equations
16:20-17:00 Aifang Qu
A Two-dimensional Piston Problem for the Chaplygin Gas
17:00-17:40 Shangkun Weng Singularity Formation for the Incompressible Hall-MHD Equations without Resistivity
18:00 Dinner
2015 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
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June 3 , Day 2: Lecture Hall, Department of Mathematics
Morning Session
Session 1 Chair: Marshall Slemrod
08:30-09:10 Shuichi Kawashima Mathematical Entropy and Euler-Cattaneo-Maxwell System
09:10-09:50 Paolo Secchi Approximate Current-vortex Sheets near the Onset of Instability
09:50-10:30 Jiahong Wu The Two-dimensional Boussinesq Equations with Partial Dissipation
10:30-10:50 Tea Break
Session 2 Chair: Ya-Guang Wang
10:50-11:30 Reinhard Racke Thermoviscoelastic Transmission Problems: Non-Exponential and olynomial Stability
11:30-12:10 Yoshiyuki Kagei On the instability of Poiseuille Flow in Viscous Compressible Fluid
11:30-12:10 Lunch Break
Afternoon Session
Session 1 Chair: Reinhard Racke
14:00-14:40 Andrea Corli
Global Weak Solutions for a Model of Two-phase Flow with Few Interfaces
14:40-15:20 Wen Shen Global Riemann Solver for Gas Flooding in Reservoir Simulation
15:20-15:40 Tea Break
Session 2 Chair: Paolo Secchi
15:40-16:20 Hermano Frid Some Questions and Results on Generalized Almost Periodic Homogenization of Nonlinear PDES
16:20-17:00 Yue-Jun Peng
Uniform Well-posedness for Partially Dissipative Hyperbolic Systems
17:00-17:40 Renjun Duan
The Vlasov-Poisson-Boltzmann System around a Nontrivial Profile
18:00 Dinner
2015 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
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June 4 , Day 3: Lecture Hall, Department of Mathematics
Morning Session
Session 1 Chair: Shuichi Kawashima
08:30-09:10 Eduard Feireisl
On Well-posedness Problems in Fluid Dynamics
09:10-09:50 Alexis F. Vasseur
Existence of Global Solutions for 3D Compressible Navier-Stokes
Equations with Degenerate Viscosities
09:50-10:30 Ronghua Pan
Shock Formation in Compressible Euler Equations
10:30-10:50 Tea Break
Session 2 Chair: Eduard Feireisl
10:50-11:30 Dehua Wang The Gauss-Codazzi Equations for Isometric Immersions of Surfaces
11:30-12:10 Chunpeng Wang Smooth Transonic Flows in De Laval Nozzles
12:10-14:00 Lunch Break
Afternoon Session
Session 1 Chair: Dehua Wang
14:00-14:40 Myoungjean Bae
The Prandtl-Meyer Reflection for Supersonic Flow Impinging onto a Solid
Wedge
14:40-15:20 Wei Xiang
Convexity of Shocks in the Self-similar Coordinates
15:20-15:40 Tea Break
Session 2 Chair: Weike Wang
15:40-16:20 Wancheng Sheng The Two Dimensional Gas Expansion Problem of the Euler equations for the Generalized Chaplygin Gas
16:20-17:00 Tong Li
Global Entropy Solutions to a Quasilinear Hyperbolic System Modeling Blood
Flow
17:00-17:40 Youshan Tao Toward a New Critical Mass Phenomenon in a Chemotaxis Model with Indirect Signal Production
18:00 Dinner
2015 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
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June 5 , Day 4: Lecture Hall, Department of Mathematics
Morning Session
Session 1 Chair: Hailiang Li
08:30-09:10 Stefano Modena
A Quadratic Interaction Estimate for Systems of Conservation Laws
09:10-09:50 Athanasios Tzavaras
Relative Entropies for the Euler-Korteweg System and Some of Its
Applications
09:50-10:30 Shu Wang
On an Axisymmetric Model for the 3D Incompressible Euler and Navier-
Stokes Equations
10:30-10:50 Tea Break
Session 2 Chair: Athanasios Tzavaras
10:50-11:30 Hailiang Li Spectrum Structure and Behaviors of Vlasov-Poisson(Maxwell)-Boltzmann Equations
11:20-12:00 Yuming Qin Global Existence and Asymptotic Behavior of Spherically Symmetric Solutions for the Multi-dimensional Infrarelativistic Model
11:30-12:10 Lunch Break
Afternoon Session
13:00- Half-day Break
18:00 Dinner
2015 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
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June 6, Day 5: Lecture Hall, Department of Mathematics
Morning Session
Session 1 Chair: Alexis F. Vasseur
08:30-09:10 Tao Luo On the Physical Gas-vacuum Interface Problem of Compressible Euler Equations with Damping
09:10-09:50 Chongchun Zeng
Instability and Exponential Dichotomy of Hamiltonian PDEs
09:50-10:30 Deane Yang
The Logarithmic Minkowski Problem
10:30-10:50 Tea Break
Session 2 Chair: Ronghua Pan
10:50-11:30 Gilles Carbou Stability of Walls in Ferromagnetic Nanowires
11:20-12:00 Hongjun Yu Large Time Behavior of Some Dissipative PDES.
11:30-12:10 Lunch Break
Afternoon Session
Session 1 Chair: Qiang Du
14:00-14:40 Jiequan Li Oscillations and Dissipations for Accurate Approximations to Hyperbolic Problems
14:40-15:20 Xianpeng Hu Wellposedness of Self-gravitating Hookean Elastodynamics
15:20-15:40 Tea Break
Session 2 Chair: Yue-Jun Peng
15:40-16:20 Beixiang Fang Global Stability of E-H Type Regular Refraction of Shocks on the Interface between Two Media
16:20-17:00 Qilong Gu Exact Boundary Controllability on a Network of Timoshenko Beams
17:00-17:40 Mijia Lai On the Best Pinching Constant on Spheres with Conic Singularities
18:00 Dinner
2015 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
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June 7, Day 6: Lecture Hall, Department of Mathematics
Morning Session
Session 1 Chair: Hermano Frid
08:30-09:10 Wen-An Yong
Conservation-Dissipation Formalism of Non-equilibrium
Thermodynamics and Its Classical Hydrodynamic Limit
09:10-09:50 Xiaozhou Yang New Scheme for Deflagration Combustion Waves
09:50-10:30 Ting Zhang
Regularity of 3D Axisymmetric Navier-Stokes Equations
10:20-10:50 Tea Break
Session 2 Chair: Chun Liu
10:50-11:30 Chunjing Xie
Well/ill-posedness for the Euler System with Source Term
11:20-12:00 Hao Wu Analysis of the Modified Phase-field Crystal Equation
11:30-12:10 Lunch Break
Afternoon Session
Session 1 Chair: Tao Luo
14:00-14:40 Yong Zhou Some Recent Studies on the Generalized MHD and Hall-MHD Systems
14:40-15:20 Tristan Buckmaster Onsagers Conjecture
15:20-15:40 Tea Break
Session 2 Chair: Yachun Li
15:40-16:20 Hairong Yuan On Transonic Shocks in Steady Compressible Euler Flows
16:20-17:00 Shuyi Zhang
Phase Transitions in a Non-isothermal van der Waals Fluid
17:00-17:40 Vincent Munnier Integral Characterization of the Hasjlasz-Sobolev Spaces on Metric Measure Spaces.
18:00 Dinner
2015 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
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Abstracts
The Prandtl-Meyer Reflection for Supersonic FlowImpinging onto a Solid Wedge
Myoungjean BaePohang University of Science and Technology, Korea
Prandtl (1936) first employed the shock polar analysis to show that, when asteady supersonic flow impinges a solid wedge whose angle is less than a criticalangle (i.e., the detachment angle), there are two possible configurations: theweak shock solution and the strong shock solution, and conjectured that theweak shock solution is physically admissible since it is the one observed experi-mentally. The fundamental issue of whether one or both of the strong and theweak shocks are physically admissible has been vigorously debated over severaldecades and has not yet been settled in a definite manner. In this talk, thislongstanding open issue is addressed, and I present analysis to establish thestability theorem for steady weak shock solutions as the long-time asymptoticsof unsteady flows for all the physical parameters up to the detachment angle forpotential flow.This talk is based on joint work with Gui-Qiang G. Chen (Univ. of Oxford) andMikhail Feldman (Univ. of Wisconsin-Madison).******************************************************************
A Lipschitz Metric for the Flow of a Nonlinear WaveEquation
Alberto BressanThe Penn State University, USA
For the nonlinear wave equation utt−c(u)(c(u)ux)x = 0, unique solutions whichconserve the total energy can be constructed globally in time, in the spaceH1(R). While the H1 norm can be constant along each solution, the H1 dis-tance between two solutions can vary wildly in time. Typically, this happenswhen energy becomes concentrated as a point mass. This talk will discuss analternative approach to the analysis of continuous dependence, constructing aRiemann-typedistance which renders the flow Lipschitz continuous. At theinfinitesimal level, the distanceis determined by the cost of an optimal trans-portation problem. The actual construction of this geodesic distance relies onthe existence of a dense set of paths of initial data, generating piecewise smoothsolutions.******************************************************************
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Onsagers Conjecture
Tristan BuckmasterCourant Institute of Mathematical Sciences, New York University, USA
In 1949, Lars Onsager in his famous note on statistical hydro-dynamics conjec-tured that weak solutions to the Euler equation belonging to Holder spaces withHlder exponent greater than 1/3 conserve energy; conversely, he conjectured theexistence of solutions belonging to any Holder space with exponent less than 1/3which dissipate energy.The first part of this conjecture has since been confirmed (cf. Eyink 1994,Con-stantin, E and Titi 1994). During this talk we will discuss recent work byCamillo De Lellis, Laszlo Szekelyhidi Jr., Philip Isett and myself related to re-solving the second component of Onsagers conjecture. In particular, we willdiscuss the construction of weak non-conservative solutions to the Euler equa-tions whose Holder 1/3− ε norm is Lebesgue integrable in time.******************************************************************
Stability of Walls in Ferromagnetic Nanowires
Gilles CarbouUniversite de Pau et des Pays de l’Adour, France
Ferromagnetic nanowires are wildly used for data recording. In such devices,the magnetization is organized in domains in which the magnetic moment is inthe direction of the wire, either in one sense or in the other one. These domainsare separated by thin zones called walls. The stability of these walls is crucialin order to ensure the reliability and the good conservation of the recorded data.The magnetization of ferromagnetic materials is modeled by the Landau-Lifschitzequation. It is a non linear parabolic partial differential equation which solutionstake their values in the unit sphere. In this talk we deal with one dimensionalLaudau-Lifschitz equation modeling ferromagnetic nanowires. We establish thestability of walls configurations in several cases: infinite or finite wires, pinchedor curved wires.******************************************************************
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Global Weak Solutions for a Model of Two-phase Flowwith Few Interfaces
Andrea CorliUniversity of Ferrara, [email protected]
The global existence of weak solutions to hyperbolic systems of conservationlaws for large initial data is a challenging problem that still lacks of generalresults. In this talk I shall present some recent results on this topic in the caseof the system
vt − ux = 0,
ut + p(v, λ)x = 0,
λt = 0
This system is a model for a isothermal fluid flow in presence of liquid-vaporphase transitions: above, t > 0 and x ∈ R, v > 0 denotes the specific volume,
u the velocity, p(v, λ) = a2
v the pressure, λ ∈ [0, 1] the mass-density fraction ofthe vapor in the fluid.First, we focus on the special case of initial data consisting of two differentphases separated by a single interface [1]. Then, we deal with the cases appear-ing when two interfaces are present [2,3]; more complicated situations can betackled in an analogous way.In all cases, we find explicit bounds on the (possibly large) initial data in orderthat weak entropic solutions exist for all times. In the case of two interfacesa stability condition is also required. The proofs exploit a carefully tailoredversion of the front-tracking scheme.
References
[1] D. Amadori, P. Baiti, A. Corli and E. Dal Santo. Global weak solutionsfor a model of two-phase flow with a single interface. J. Evol. Equationsto appear, 2015.
[2] D. Amadori, P. Baiti, A. Corli and E. Dal Santo. Global existence ofsolutions for a multi-phase flow: a drop in a gas-tube. Submitted, 2015.
[3] D. Amadori, P. Baiti, A. Corli and E. Dal Santo. Global existence ofsolutions for a multi-phase flow: a bubble in a liquid tube and relatedcases. Submitted, 2015.
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Nonlocal Balance Laws and Their NumericalApproximations
Qiang DuThe Penn State University, USA
Nonlocality is ubiquitous in nature. We present some nonlocal balance lawsthat may be seen as generalizations to classical, local balance equations. Thesenonlocal equations not only recover local models as nonlocality vanishes but alsoallow more general interactions and preserve more physical features than theirlocal counterparts. We also discuss the convergence of numerical algorithms.******************************************************************
The Vlasov-Poisson-Boltzmann System around aNontrivial Profile
Renjun DuanThe Chinese University of Hong Kong, Hong Kong
The talk is devoted to the study of the time-asymptotic stability of rarefactionwaves for the Vlasov-Poisson-Boltzmann system in the whole space with slabsymmetry. The large time profile of the electric potential can take distinct con-stant states at both far-fields. The rarefaction wave is constructed through thequasineutral Euler equations which are the zero-order fluid dynamic approxima-tion of the kinetic system. The key point in the proof is motivated by the studyof the same problem for the viscous compressible fluid with the self-consistentelectric field. The ratio of masses of two species particles plays a role in theconstruction and stability analysis of such nontrivial profile.******************************************************************
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Global Stability of E-H Type Regular Refraction ofShocks on the Interface between Two Media
Beixiang FangShanghai Jiao Tong University, China
In this talk I will discuss the refraction of shocks on the interface for 2-d steadycompressible flow. Particularly, the class of E-H type regular refraction is de-fined and its global stability of the wave structure is verified. The 2-d steadypotential flow equations is employed to describe the motion of the fluid. Thestability problem of the E-H type regular refraction can be reduced to a freeboundary problem of nonlinear mixed type equations in an unbounded domain.The corresponding linearized problem has similarities to a generalized Tricomiproblem of the linear Lavrentiev-Bitsadze mixed type equation, and it can bereduced to a nonlocal boundary value problem of an elliptic system. The lateris finally solved by establishing the bijection of the corresponding nonlocal op-erator in a weighted Holder space via careful harmonic analysis. This is a jointwork with CHEN Shuxing and HU Dian.******************************************************************
On Well-posedness Problems in Fluid Dynamics
Eduard FeireislThe Academy of Sciences of Czech Republic, Czech Republic
We discuss well-posedness of certain problems in the theory of inviscid fluids.Suitable admissibility criteria are proposed based on the viscosity limits. Sev-eral examples including the complete system describing a compressible heatconducting fluid are presented.******************************************************************
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Some Questions and Results on Generalized AlmostPeriodic Homogenization of Nonlinear PDES
Hermano FridInstituto de Matemtica Pura e Applicada-IMPA, Brazil
We recall some recent results about homogenization of nonlinear partial differen-tial equations in the context of ergodic algebras. We review the concept of two-scale Young measures in generalized almost periodic homogenization and someimportant applications in which its use demonstrates to be a decisive resourcefor the homogenization analysis, among which the porous medium equationand some correlated ones. We also discuss the relationship between generalizedalmost periodic homogenization and stationary ergodic stochastic homogeniza-tion, and we exemplify this with the Hamilton-Jacob and fully nonlinear ellipticand parabolic equations. Parts of this research were done in collaboration withLuigi Ambrosio, Jean Silva e Henrique Versieux.******************************************************************
Exact Boundary Controllability on a Network ofTimoshenko Beams
Qilong GuShanghai Jiao Tong University, China
In this talk, we consider the exact boundary controllability on Timoshenkobeams. The basic idea is a constructive method, which is usually used to dealwith the exact boundary controllability for general hyperbolic systems. Gener-ally, we suppose the eigen values and the eigen vectors are C1. However, this isnot satisfied in our model. And we consider both the models with and withoutthe gravity.******************************************************************
Wellposedness of Self-gravitating Hookean Elastodynamics
Xianpeng HuCity University of Hong Kong, Hong Kong
This talk is devoted to the well posedness issue for the self-gravitating Hookeanelastodynamics in dimension three. The solution is constructed near an equi-librium.******************************************************************
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On the Instability of Poiseuille Flow in ViscousCompressible Fluid
Yoshiyuki KageiKyushu University, Japan
We consider the stability of plane Poiseuille flow in viscous compressible fluid inan infinite layer. It will be shown that the plane Poiseuille flow is asymptoticallystable under disturbances sufficiently small in some Sobolev space provided thatthe Reynolds and Mach numbers are small enough. A condition for the Reynoldsand Mach numbers will then be given in order for plane Poiseuille flow to beunstable. It will be shown that plane Poiseuille flow is unstable for Reynoldsnumbers much less than the critical Reynolds number for the incompressibleflow when the Mach number is suitably large. We will also discuss bifurcationof traveling waves from Poiseuille flow.******************************************************************
Mathematical Entropy and Euler-Cattaneo-MaxwellSystem
Shuichi KawashimaKyushu University, Japan
The notion of the mathematical entropy was first introduced by Godunov (in1961) for hyperbolic systems of conservation laws. The notion was then extendedby Kawashima-Shizuta (in 1988) for hyperbilic-parabolic systems of conserva-tion laws and by Kawashima-Yong [1] (in 2004) for hyperbolic systems of balancelaws with symmetric relaxation.In this talk, we modify the definition of the mathematical entropy in [1] so thatit is valid for systems with non-symmetric relaxation. As an example we pro-pose the Euler-Cattaneo-Maxwell system whose thermal effect is described bythe Cattaneo law. Then we investigate the dissipative structure of that systemand observe that it is of the regularity-loss type as in the simpler Euler-Maxwellsystem. Moreover, we show the global existence and stability of solutions forsmall initial data.These results are based on the recent joint work with Yoshihiro Ueda.
References
[1] S. Kawashima and W.-A. Yong, Dissipative structure and entropy forhyperbolic systems of balance laws, Arch. Rational Mech. Anal., 174(2004), 345-364.
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On the Best Pinching Constant on Spheres with ConicSingularites
Mijia LaiShanghai Jiao Tong University, China
In this talk, I will report my recent joint work with Hao Fang on the best pinch-ing constant on spheres with conic singularities. There are renewed interestsin metrics with conic singularites after the seminal work of Troyanov. Whileon spheres and all cone angles are restricted to (0, 2π), necessary and suffi-cient conditions for the existence of constant positive curvature are obtainedthrough works of Troyanov, Luo-Tian, Chen-Li. It thus left open the questionof determining the best pinching constant (Kmin/Kmax) on spheres with conicsingularities which does not admit constant positive cruvature. We give an an-swer to this question. The pinching constant is tied closely with the cone angles.For multiple conic points, there is a similar collapsing phenomenon comparingwith the Ricci flow on conic spheres.******************************************************************
Global WP of Incompressible Elastodynamics in 2D
Zhen LeiFudan University, [email protected]
We report our recent results on the incompressible Navier-Stokes equations,including constructing large general solutions, pointwise a priori estimate ofaxisymmetric solutions and criticality of the axisymmetric Navier-Stokes equa-tions.******************************************************************
Data Compatibility for 3-D Euler Equations
Dening LiWest Virginia University, USA
We study the compatibility of the Cauchy data which have a jump discontinuityfor the non-isentropic 3-d Euler system. For a complete range of combinationsof waves including shocks, rarefaction waves, and contact discontinuity, it isshown that the data is compatible of in finite order if the corresponding 1-dRiemann problem admits such a solution.******************************************************************
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Spectrum Structure and Behaviors ofVlasov-Poisson(Maxwell)-Boltzmann Equations
Hailiang LiCapital Normal University, [email protected]
We present the recent results on the spectrum structures of the Vlasov-Poisson(Maxwell)-Boltzmann equations and justify the influences of the electrostaticpotential force, Lorentz force, and the mutual interaction between charged par-ticles pf differernt type.It is joint with Mingying Zhong and Tong Yang.******************************************************************
Oscillations and Dissipations for AccurateApproximations to Hyperbolic Problems
Jiequan LiBeijing Normal University, China
The Gibbs phenomenon is well-known when discontinuous functions are ap-proximated by sections of Fourier series. Analogous oscillations occur ubiqui-tously when hyperbolic problems are approximated accurately since the solu-tions contain discontinuities (e.g. shocks, vortices) in general; the oscillationsare produced due to large phase errors and insufficient numerical dissipations, ascommonly understood. Hence artificial numerical viscosity has to be added inorder to suppress the superfluous oscillations, thanks to von Neumann, and thisapproach guides the development of CFD more than half a century. However,recent studies show that the dissipation mechanisms of numerical schemes arequite subtle and depend on the range of frequency modes quantitatively: Thetraditional artificial viscosity approach just works well for small phase errors.In order to suppress large phase errors due to high frequency modes (e.g che-querboard modes), a more dissipative numerical damping is introduced. Usingthe language of modified equations of numerical schemes, numerical dissipationsare now distinguished as numerical damping and numerical viscosity, which cor-respond to the effects governed by ODEs and second order diffusion equations,respectively, to regularize numerical solutions. This distinction can effectivelyhelp to understand the dissipation properties of a numerical scheme when itaccurately solves hyperbolic problems.In this talk, I will report some recent results and describe some possible appli-cations.******************************************************************
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Global Entropy Solutions to a Quasilinear HyperbolicSystem Modeling Blood Flow
Tong LiThe University of Iowa, USA
This talk is concerned with an initial-boundary value problem on bounded do-mains for a one dimensional quasilinear hyperbolic model of blood flow withviscous damping. It is shown that L∞ entropy weak solutions exist globally intime when the initial data are large, rough and contains vacuum states. Further-more, based on entropy principle and the theory of divergence measure field, itis shown that any L∞ entropy weak solution converges to a constant equilibriumstate exponentially fast as time goes to infinity. The physiological relevance ofthe theoretical results obtained in this paper is demonstrated. This is a jointwork with Kun Zhao.******************************************************************
Energetic Variational Approaches for Transport ofCharged Particles.
Chun LiuPenn State University, USA
Almost all biological activities involve transport of charged ions in specific bio-logical environments. In this talk, I will discuss a unified energetic variationalapproach developed specifically for these multiscale-multiphysics problems. Iwill discuss the relevant classical theories and relevant physical approaches andmethods. I will focus on the mathematics, in particular the analytical issuesarising from these studies.******************************************************************
On the Physical Gas-Vacuum Interface Problem ofCompressible Euler Equations with Damping
Tao LuoGeorgetown University, USA
In this talk, I will present the results on the global regularity and large timeconvergence of solutions to the physical gas-vacuum interface problem of com-pressible Euler Equations with damping featuring the behavior that the soundspeed 1/2-Holder continuous near the vacuum boundary.This is a joint work with Huihui Zeng.
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A Quadratic Interaction Estimate for Systems ofConservation Laws
Stefano ModenaSissa, Italy
The first result about existence of solutions to the system of conservation laws{ut + f(u)x = 0,
u(0, x) = u0(x), f : Rn → Rnstrictly hyperbolic, Tot.Var.(u0)� 1.(1)
is contained in the celebrated paper [2] by J. Glimm, later improved by T.-P.Liu in [3], where a sequence {uε}ε of approximate solutions, which converge (upto subsequences) to the entropic solution u of (1), is constructed. In [1] Glimm’sresult is further improved, showing that the approximation sequence {uε}ε canbe chosen in such a way that its rate of convergence is equal to
‖uε(t, ·)− u(t, ·)‖1 = o(1)√ε|log(ε)|. (2)
All the previous results are based on careful interaction estimates on the el-ementary waves present in the approximations uε. However, they work onlyunder the restrictive assumption that each characteristic field of Df is eithergenuinely non linear or linearly degenerate.Aim of my talk is to present a new interaction estimate on the total variationin time of the speeds of the elementary waves in uε, which works in the mostgeneral case, where no assumption on f is made except its strict hyperbolicity,and which can thus be used to prove that also in the general setting the Glimm’sapproximate solutions {uε}ε converge to the entropic solution u of (1) and thesame rate of convergence (2) holds.This is a joint work with Stefano Bianchini.
References
[1] A. Bressan, A. Marson Error Bounds for a Deterministic Version of theGlimm Scheme, Arch. Rational Mech. Anal. 142 (1998), 155-176.
[2] J. Glimm, Solutions in the Large for Nonlinear Hyperbolic Systems ofEquations, Comm. Pure Appl. Math. 18 (1965), 697-715.
[3] T.-P. Liu, The deterministic version of the Glimm scheme, Comm. Math.Phys. 57 (1977), 135-148.
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Integral Characterization of the Hasjlasz-Sobolev Spaceson Metric Measure Spaces
Vincent MunnierShanghai Jiao Tong University, China
This work is motivated by a paper of Bourgain, Brezis and Mironescu. In thispaper, the authors give a new insight onclassical Sobolev spaces. They estab-lish new compactness results for Sobolev spaces. They prove as well that theSobolev (semi-)norm on W 1,p is a scaled limit of the W s,p (semi-)normwhen sgo to 1. This quantitative statement allows them to establish refined Poincarinequalities.In this talk, we want to discuss the same but for a natural class of metric measurespaces (X, d, µ) (those supportingan Ahlfors regular µ satisfying weak Poincarinequalities). First, how to define the analogue of the Sobolev spaces on metricspaces? The Hasjlasz-Sobolev spaces are a natural candidate.What can we say if the measure µ is not translation invariant? According to aresult of Cheeger, these metric measure spaces carry a ”differential” structure.This will be the occasion to speak about ”Cheeger differentiation” and to showhow to use abstract differentiation results to establish the integral characteriza-tion of the Hajlasz-Sobolev spaces. Finally, we will give some examples and wewill speak about further generalizations.******************************************************************
Shock Formation in Compressible Euler Equations
Ronghua PanGeorgia Institute of Technology, USA
It is well-known that shock will form in finite time for hyperbolic conservationlaws from initial compression no matter how small and smooth the data are.Classical results, including P. D. Lax(1964), T. Liu(1979), Li-Zhou-Kong(1994),confirms that when initial data are small smooth perturbation near constantstates, finite blowup in gradient occurs if and only if initial data contains anycompression in some truly nonlinear characteristic field. A natural puzzle isthat: Will this picture keep true for large data for physical system such asCompressible Euler equations? One of the key issues is how to find an effectiveway to obtain sharp enough control on density lower bound. For isentropic flow,we offer a complete picture on the finite time shock formation from smooth ini-tial data away from vacuum, which is consistent with small data theory. For
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adiabatic flow, we show a striking observation that weak compressions do notnecessarily develop singularity in finite, in sharp contrast to the small data the-ory. Furthermore, we prove that relatively strong compression do develop finitesingularity. These lectures are based on joint with G. Chen and S. Zhu.******************************************************************
Uniform Well-posedness for Partially DissipativeHyperbolic Systems
Yue-Jun PengUniversite Blaise Pascal, [email protected]
We consider smooth solutions for first-order partially dissipative hyperbolic sys-tems with relaxation, which are written in non-conservative form in severalspace dimensions. Under usual stability conditions, we show global existencewith small initial data when the relaxation time is fixed and the space dimen-sion is greater than 3. Further stability conditions are discussed to yield theuniform global well-posedness with respect to the relaxation time. These con-ditions imply also compactness of the solution sequences and the convergenceof the systems to nonlinear parabolic systems. Various examples are given asapplications of the results.******************************************************************
Global Existence and Asymptotic Behavior of SphericallySymmetric Solutions for the Multi-dimensional
Infrarelativistic Model
Yuming QinDonghua University, China
In this talk, we establish the global existence, uniqueness and asymptotic behav-ior of spherically symmetric solutions for the multi-dimensional infrarelativisticmodel in Hi ×Hi ×Hi ×Hi+1(i = 1, 2, 4).
References
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[1] C. Buet and B. Despres, Asymptotic analysis of fluid models for the cou-pling of radiation and hydrodynamics, J. Quant. Spectroscopy RadiativeTransfer, 85 (2004), 385-418.
[2] S. Chandrasekhar, Radiative Transfer, Dover Publications, Inc., New York,1960.
[3] B.Dubroca and J.L.Feugeas, Etude theorique et numerique d’une hierarchiede modeles aux moments pour le transfert radiatif, Comptes Rendus deI’Academie des Sciences, Serie I, 329 (1999), 915-920.
[4] B. Ducomet and S. Necasova, Large-time behavior of the motion of aviscous heat-conducting one-dimensional gas coupled to radiation, Annalidi Matematica, 191 (2012), 219-260.
[5] B. Ducomet and S. Necasova, Asymptotic behavior of the motion of a vis-cous heat-conducting one-dimensional gas with radiation: the pure scat-tering case, Analysis and Applications, 11(1) (2013), 1350003(29 pages).
[6] F. Golse and B. Perthame, Generalized solutions of the radiative transferequations in a singular case, Comm. Math. Physics, 106 (1986), 211-239.
[7] Y. Li and S. Zhu, Formation of singularities in solutions to the com-pressible radiation hydrodynamics equations with vacuum, J. DifferentialEquations, 256 (2014), 3943-3980.
[8] C.Lin,Mathematical analysis of radiative transfer models,Ph.D.Thesis, 2007.
[9] C. Lin, J. F. Coulombel and T. Goudon, Shock profiles for non-equilibriumradiating gases, Physics D, 218 (2006), 83-94.
[10] R. B. Lowrie, J. E. Morel and J. A. Hittinger, The coupling of radiationand hydrodynamics, Astrophysical Journal, 521 (1999), 432-450.
[11] G. C. Pomraning, The Equations of Radiation Hydrodynamics, PergamonPress, New York, Oxford, 1973.
[12] G. C. Pomraning, Radiation Hydrodynamics, Dover Publications, Inc.,Mineola, New York, 2005.
[13] Y. Qin, Nonlinear Parabolic-Hyperbolic Coupled Systems and Their At-tractors, Volume 184, Advances in Partial Dierential Equations, BirkhauserVerlag AG, Basel-Boston-Berlin, 2008.
[14] Y. Qin and L. Huang, Global well-Posedness of Nonlinear Parabolic-Hyperbolic Coupled Systems, Frontiers in Mathematics, Springer BaselAG, 2012.
[15] Y. Qin, X. Liu and T. Wang, Global well-Posedness of Nonlinear Evolu-tionary Fluid Equations, Frontiers in Mathematics, Springer Basel AG,2015.
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[16] Y. Qin, B. Feng and M. Zhang, Large-time behavior of solutions for theone-dimensional infrarelativistic model of a compressible viscous gas withradiation, J. Dierential Equations, 252 (2012), 6175-6213.
[17] Y. Qin, B. Feng and M. Zhang, Large-time behavior of solutions for the1D viscous heat-conducting gas with radiation: the pure scattering case,J. Dierential Equations, 256 (2014), 989-1042.
[18] S. F. Shandarin and Y. B. Zeldovichi, The large-scale structure of the uni-verse: Turbulence, intermittency, structures in a self-gravitating medium,Rev. Modern Phys., 61 (1989), 185-220.
[19] X. Zhang and S. Jiang, Local existence and nite-time blow-up in multi-dimensional radiation hydrodynamics, J. Math. Fluid Mech., 9 (2007),543-564.
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A Two-dimensional Piston Problem for the Chaplygin Gas
Aifang QuWuhan Institute of Physics and Mathematics, CAS, China
In this talk, we consider a piston problem for the unsteady two-dimensionalEuler system for a Chaplygin gas. The piston is assumed to proceed or recedeto a static gas with uniform velocity. The global existence of solution to a largeclass of initial data as well as the inclined angle of the piston. The structureof the solutions are described in detail. Attached wave is present for the con-vex piston proceeding to the gas with initial supersonic velocity, while detachedwaves are discussed in other cases. This problem could also be considered as atwo-dimensional Riemann boundary value problem.******************************************************************
Thermoviscoelastic Transmission Problems:Non-Exponential and Polynomial Stability
Reinhard RackeUniversity of Konstanz, [email protected]
We investigate transmission problems between a (thermo-)viscoelastic systemwith Kelvin-Voigt damping, and a purely elastic system. It is shown that nei-ther the elastic damping by Kelvin-Voigt mechanisms nor the dissipative effect
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of the temperature in one material can assure the exponential stability of thetotal system when it is coupled through transmission to a purely elastic system.The approach shows the lack of exponential stability using Weyls theorem onperturbations of the essential spectrum. Instead, strong stability can be shownusing the principle of unique continuation. To prove polynomial stability weprovide an extended version of the characterizations by Borichev and Tomilov.Observations on the lack of compacity of the inverse of the arising semigroupgenerators are included too. The results apply to thermo-viscoelastic systems,to purely elastic systems as well as to the scalar case consisting of wave equa-tions.
References
[1] Munoz Rivera, J.E., Racke, R.: Transmission problems in (thermo-)visco-elasticity with Kelvin-Voigt damping: non-exponential, strong and poly-nomial stability. Preprint (2015).
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Approximate Current-vortex Sheets near the Onset ofInstability
Paolo SecchiUniversity of Brescia, [email protected]
In this talk I present a recent result about the free boundary problem for 2Dcurrent-vortex sheets in ideal incompressible magneto-hydrodynamics near thetransition point between the linearized stability and instability. In order to studythe dynamics of the discontinuity near the onset of the instability, Hunter andThoo have introduced an asymptotic quadratically nonlinear integro-differentialequation for the amplitude of small perturbations of the planar discontinuity.We study such amplitude equation and prove its nonlinear well-posedness undera stability condition given in terms of a longitudinal strain of the fluid alongthe discontinuity.This is a joint work with A.Morando and P.Trebeschi.******************************************************************
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Global Riemann Solver for Gas Flooding in ReservoirSimulation
Wen ShenThe Penn State University, USA
shen [email protected]
In this talk we consider the model for gas flooding with three component. Theresulting model is a 2 × 2 system of conservation law. The model is known tobe non-hyperbolic, with various degeneracies. These include a curve and anarea of linearly degeneracy, two curves of parabolic degeneracy. We present aconstruction of the global Riemann Solver, which takes advantage of the under-lining splitting property of the thermo-dynamics from the hydro-dymanics.This is a joint work with S. Khorsandi and R. Johns, both from Department ofEnergy and Mineral Engineering, Penn State University.******************************************************************
The Two Dimensional Gas Expansion Problem of theEuler Equations for the Generalized Chaplygin Gas
Wancheng ShengShanghai University, [email protected]
The collapse of a wedge-shaped dam containing fluid initially with a uniformvelocity can be described as an expansion problem of gas into vacuum. It isan important class of binary interaction of rarefaction waves in the two dimen-sional Riemann problems for the compressible Euler equations. In this paper,we present various characteristic decompositions of the two dimensional pseudo-steady Euler equations for the generalized Chaplygin gas and obtain some prioriestimates. By these estimates, we prove the global existence of solution to theexpansion problem of a wedge of gas into vacuum with the half angle θ ∈ (0, π/2)for the generalized Chaplygin gas.******************************************************************
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The Problem with Hilbert’s 6th Problem
Marshall SlemrodUniversity of Wisconsin, USA
In his famous 1900 ICM address Hilbert suggested that mathematicians addressthe issue of obtaining a rigorous derivation of laws of macroscopic continuumgas dynamics from the Boltzmann equation of the kinetic theory of gases. Inthis talk I will address Hilbert’s problem ( the 6th problem in his address) andsuggest that based on analysis, laboratory experiment, and computer simulationHilbert’s goal is not achievable.******************************************************************
Toward a New Critical Mass Phenomenon in aChemotaxis Model with Indirect Signal Production
Youshan TaoDonghua University, China
This talk addresses a chemotaxis system with indirect signal production, whichmodels the aggregation behavior of the Mountain Pine Beetle in forest habitat.It is shown that this system exhibits a novel type of critical mass phenomenonwith regard to the formation of singularities, which drastically differs from thewell-known threshold property of the classical Keller-Segel system, in that itrefers to blow-up in infinite time rather than in finite time. This is a joint workwith Michael Winkler (Paderborn).******************************************************************
Relative Entropies for the Euler-Korteweg System andSome of Its Applications
Thanos TzavarasKing Abdullah University of Science and Technology, Kingdom of Saudi Arabia
We review the relative entropy method in a setup where the flow is caused by afunctional. The relatve entropy is then naturally defined by taking the Taylorexpansion of the relevant functional. As applications we pursue: weak-stronguniqueness for the Euler-Korteweg system, stability for phase transitions andconvergence from Euler-Korteweg with friction in the diffusive limit to gradientflows.(joint work with C. Lattanzio and J. Giesselmann)******************************************************************
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Existence of Global Solutionsfor 3D CompressibleNavier-Stokes Equations with Degenerate Viscosities
Alexis F. VasseurUniversity of Texas at Austin. USA
We prove the existence of global weak solutions for 3D compressible Navier-Stokes equations with degenerate viscosities. The method is based on the Breschand Desjardins entropy. The main contribution is to derive the Mellet-Vasseurtype inequality for the weak solutions, even if it is not verified by the first levelof approximation. This provides existence of global solutions in time, for thecompressible Navier-Stokes equations, for any γ > 1 in three dimensional space,with large initial data possibly vanishing on the vacuum. This is a joint workwith Cheng Yu.******************************************************************
Smooth Transonic Flows in De Laval Nozzles
Chunpeng WangJilin University, [email protected]
This talk concerns smooth transonic flows of Meyer type in de Laval nozzles,which are governed by an equation of mixed type with degeneracy and singu-larity at the sonic state. First we study the properties of sonic curves. For anyC2 transonic flow of Meyer type, the set of exceptional points is shown to bea closed line segment (may be empty or only one point). Furthermore, it isproved that a flow with nonexceptional points is unstable for a C1 small per-turbation in the shape of the nozzle. Then we seek smooth transonic flows ofMeyer type which satisfy physical boundary conditions and whose sonic pointsare exceptional. For such a flow, its sonic curve must be located at the throatof the nozzle and it is strongly singular in the sense that the sonic curve is acharacteristic degenerate boundary in the subsonic-sonic region, while in thesonic-supersonic region all characteristics from sonic points coincide, which arethe sonic curve and never approach the supersonic region. It is proved that thereexists uniquely such a smooth transonic flow near the throat of the nozzle, whoseacceleration is Lipschitz continuous, if the wall of the nozzle is sufficiently flat.The global extension of this local smooth transonic flow is also studied. Theworks are jointed with Professor Zhouping Xin.******************************************************************
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The Gauss-Codazzi Equations for Isometric Immersions ofSurfaces
Dehua WangUniversity of Pittsburgh, USA
The Gauss-Codazzi equations for isometric immersions of surfaces will be dis-cussed. Various approaches and recent results on global solutions for the hy-perbolic problems with negative Gauss curvatures will be presented. The talkis based on the joint works with Wentao Cao, Gui-Qiang Chen, Feimin Huang,and Marshall Slemrod.******************************************************************
On an Axisymmetric Model for the 3D IncompressibleEuler and Navier-Stokes Equations
Shu WangBeijing University of Technology, China
We study the singularity formation and global regularity of an axisymmetricmodel for the 3D incompressible Euler and Navier-Stokes equations. This 3Dmodel is derived from the axisymmetric Navier-Stokes equations with swirl us-ing a set of new variables. The model preserves almost all the properties of thefull 3D Euler or Navier-Stokes equations except for the convection term whichis neglected. If we add the convection term back to our model, we would recoverthe full Navier-Stokes equations. We prove rigorously that the 3D model devel-ops finite time singularities for a large class of initial data with finite energy andappropriate boundary conditions. Moreover, we also prove that the 3D inviscidmodel has globally smooth solutions for a class of large smooth initial data withsome appropriate boundary condition. The related problems are surveyed andsome recent results will also be reviewed.
References
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[1] Hou, Thomas Y.; Li, Congming; Shi, Zuoqiang; Wang, Shu; Yu, Xinwei.On singularity formation of a nonlinear nonlocal system. Arch. Ration.Mech. Anal. 199 (2011), no. 1, 117-144.
[2] Hou, Thomas Y.; Shi, Zuoqiang; Wang, Shu. On singularity formation ofa 3D model for incompressible Navier-Stokes equations. Adv. Math. 230(2012), no. 2,607641.
[3] Hou, Thomas Y., Lei, Z., Luo, G., Wang, Shu, Zou, C. On Finite TimeSingularity and Global Regularity of an Axisymmetric Model for the 3DEuler Equations, Arch Rational Mech. Anal., 212(2014):683-706. SeeDigital Object Identifier (DOI) 10.1007/s00205-013-0716-6.
[4] Wang, Shu. On a new 3D model for incompressible Euler and Navier-Stokes equations. Acta Mathematica Scientia.30B(6)(2010): 2089-2102.
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A One-domain Approachfor Modeling and Simulation ofFree Fluid over a Porous Medium
Xiao-Ping WangHong Kong University of Science and Technology, China
We propose a one-domain approach based on the Brinkman model for the mod-eling and simulation of the transport phenomenon between free fluid and aporous medium. A thin transition layer is introduced between the free fluidregion and the porous media region, across which the porosity and permeabilityundergo a rapid but continuous change. We study the behavior of the solu-tion to theone-domainmodel analytically and numerically. Using the method ofmatched asymptotic expansion, we recover the Beavers-Joseph-Saffman (BJS)interface condition as the thickness of the transition layer goes to zero. Wealso calculate the error estimates between the leading order solution of theone-domainmodel and the standard Darcy-Stokes model of two-domainmodel withBJS condition. Numerical methods are developed for both theone-domainmodeland the two-domainmodel. Numerical results are presented to support the ana-lytical results, thereby justifying theone-domainmodel as a good approximationto the two domainStokes-Darcy model.
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Singularity Formation for the Incompressible Hall-MHDEquations without Resistivity
Shangkun WengPohang University of Science and Technology, Korea
In this talk we show that the incompressible Hall-MHD system without resistivi-ty is not globally in time well-posed in any Sobolev space Hm(R3) for any m >72 .Namely, either the system is locally ill-posed in Hm(R3),or it is locally well-posed , but there exists an initial data inHm(R3), for which theHm(R3) norm ofsolution blows-up in finite time if m > 7
2 . In the latter case we choose an axsym-metric initial data u0(x) = u0r(r, z)er + b0z(r, z)ez and B0(x) = b0θ(r, z)eθ, andreduce the system to the axisymmetric setting. If the convection term survivessufficiently long time, then the Hall term generates the singularity on the axisof symmetry and we have lim supt→t∗ supz∈R |∂z∂rbθ(r = 0, z)| = ∞ for somet∗ > 0, which will also induce a singularity in the velocity field. This is a jointwork with Prof. Dongho Chae.
References
[1] D. Chae, S. Weng. Singularity formation for the incompressible Hall-MHD equations without resistivity. Ann. I. H. Poincare-AN (2015).http://dx.doi.org/10.1016/j.anihpc.2015.03.002.
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Analysis of the Modified Phase-field Crystal Equation
Hao WuFudan University, [email protected]
We consider the modified phase-field crystal (MPFC) equation that has recentlybeen proposed by P. Stefanovic et alto modelcrystal growth in a supercooledliquid. We analyze the MPFC equation endowed with periodic boundary condi-tions.First, we prove the global existenceand uniqueness of solutions with finiteenergy.Thenwe establish the existence of a global attractor as well asa familyof exponential attractors that are robust with respect to the relaxation time.Finally,we show that any bounded trajectory of the MPFC equation convergesto a single equilibrium as time goes to infinity.******************************************************************
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The Two-dimensional Boussinesq Equations with PartialDissipation
Jiahong WuOklahoma State University,USA
The Boussinesq equations concerned here model geophysical flows such as at-mospheric fronts and ocean circulations. Mathematically the 2D Boussinesqequations serve as a lower-dimensional model of the 3D hydrodynamics equa-tions. In fact, the 2D Boussinesq equations retain some key features of the 3DEuler and the Navier-Stokes equations such as the vortex stretching mechanism.The global regularity problem on the 2D Boussinesq equations with partial orfractional dissipation has attracted considerable attention in the last few years.This talk presents recent developments in this direction. In particular, we de-tail the global regularity result on the 2D Boussinesq equations with verticaldissipation as well as the result for the 2D Boussinesq equations with generalcritical dissipation.******************************************************************
Convexity of Shocks in the Self-similar Coordinates
Wei XiangCity University of Hong Kong, Hong Kong
Convexity of shocks is frequently observed in many experimental results andprovides better understanding of mathematical problems with the nonlinearwave, the uniqueness for instance. We consider the pseudo-transonic shock gov-erned by the potential flow equation in the self-similar coordinates, and give aframework to show the strict and uniform convexity by a nonlinear and globalargument. Finally, several applications are given. This work is done with Prof.G.-Q. Chen and Prof. Feldman.******************************************************************
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Well/ill-posedness for the Euler System with Source Term
Chunjing XieShanghai Jiao Tong University, China
In this talk, we first discuss the global well-posedness of rotating shallow watersystem with the small smooth initial data, where the dispersion of the systemwas exploited. Next, we show the existence of infinitely many global weak so-lutions for the Euler system with source term, in particular, the weak solutionswith finite states.******************************************************************
The Logarithmic Minkowski Problem
Deane YangNew York University, USA
The logarithmic Minkowski problem, like the classical Minkowski problem, is afundamental question in the affine geometry of convex bodies. For symmetricconvex bodies, it asks what are the necessary and sufficient conditions for a mea-sure in (n-1)-dimensional projective space to be the cone-volume measure of theunit ball in an n-dimensional normed space. Solving this problem is equivalentto establishing existence of a solution to a Monge-Ampere equation. This talkoutlines a complete solution to the symmetric logarithmic Minkowski problemand will present related open problems.******************************************************************
New Scheme for Deflagration Combustion Waves
Xiaozhou YangWuhan Institute of Physics and Mathematics,CAS, China
In this talk, we will present a new scheme for combustion computation, usingthis scheme, we can stimulate deflagration combustion waves, we can also provethe convergence of this new scheme, an also show somefigures and videos ofseveral numerical results. This is a Joint work with Ph.D. student Chun-longYang.******************************************************************
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On Transonic Shocks in Steady Compressible Euler Flows
Hairong YuanEast China Normal University, China
I will review some recent results on the mathematical studies of transonic shocksin aerodynamics, by considering related free boundary problems of the steadycompressible full Euler system, which is a first-order system of conservation lawsof elliptic-hyperbolic composite-mixed type for the subsonic flows. Specifically Iwill introduce a result on stability of spherical transonic shocks for three dimen-sional full compressible Euler system, which used some tools from differentialgeometry to separate the nonlinear free boundary problem equivalently to sixsub-problems, involving a div-curl system on sphere, a Venttsel problem of anonlocal second order elliptic equation, and several Cauchy problems of trans-port equations. The talk is based upon joint works with many collaborators.******************************************************************
Conservation-Dissipation Formalism of Non-equilibriumThermodynamics and Its Classical Hydrodynamic Limit
Wen-An YongTsinghua University, China
We propose a conservation-dissipation formalism (CDF) for coarse-grained de-scriptions of irreversible processes. This formalism is based on a stability cri-terion for non-equilibrium thermodynamics. The criterion ensures that non-equilibrium states tend to equilibrium in long time. As a systematic methodol-ogy, CDF provides a feasible procedure in choosing non-equilibrium state vari-ables and determining their evolution equations. The equations derived in CDFhave a unified elegant form. They are globally hyperbolic, allow a convenientdefinition of weak solutions, and are amenable to existing numerics. More impor-tantly, CDF is a genuinely nonlinear formalism and works for systems far awayfrom equilibrium. With this formalism, we formulate a novel thermodynamicstheory for non-isothermal compressible Maxwell fluid flows asa typical example.The new theory generalizesMaxwell’s law in a regularized and nonlinear fash-ion. Moreover, we rigorously justify that this generalized hydrodynamic systemtends to the classical hydrodynamics when the relaxation time approaches tozero.******************************************************************
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Large Time Behavior of Some Dissipative PDEs
Hongjun YuSouth China Normal University, China
In this talk, we discuss about large time behavior of global solutions tosomedissipative PDES in nonlinear conservation laws.******************************************************************
Instability and exponential dichotomy of HamiltonianPDEs
Chongchun ZengGeorgia Institute of Technology, USA
In this talk, we start with a general linear Hamiltoniansystem ut = JLu in aHilbert space X – the energy space. Weassume that (a) J : X∗ ⊃ D(J)→ X isanti-self-adjoint and (b) L : X → X∗ is bounded, symmetric, with closed rangeR(L),and its induced energy functional 1
2 〈Lu, u〉 hasonly finitely many negativedimensions – n−(L) < ∞. Our firstresult is an index theorem related to thelinear instability ofetJL, which gives some relationship between n−(L) and thed-imensions of generalized eigenspaces of eigenvalues of JL, some ofwhich may beembedded in the continuous spectrum. In addition, foreach eigenvalue λ of JLwe also construct special “good”choice of generalized eigenvectors which bothrealize the corresponding Jordan canonical form corresponding to λ andworkwell with L. Our second result is the linear exponentialtrichotomy of the groupetJL. This includes the nonexistence of exponential growth in the finite co-dimensional invariant centersubspace and the optimal bounds on the algebraicgrowth rate there.Finally we will discuss applications to examples of nonlinearHamiltonian PDEs such as BBM, GP, and 2-D Euler equations, including theconstruction of some local invariant manifolds near some coherent states (stand-ing wave, steady state, traveling waves etc.). This isa joint work with ZhiwuLin.******************************************************************
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Phase Transitions in a Non-isothermal van der WaalsFluid
Shu-Yi ZhangShanghai University of International Business and Economics, China
zhang [email protected]
In a fluid with a non-monotonic state equation, say van der Waals fluid, non-classical shock waves like subsonic phase transition usually appear whose char-acteristics violate the well-known Lax inequalities. In this talk, we shall considerissues related to subsonic phase transitions in a non-isothermal van der Waalsfluid including admissible criterion, multi-dimensional stability and existence.******************************************************************
Regularity of 3D Axisymmetric Navier-Stokes Equations
Ting ZhangZhejiang University, [email protected]
In this talk, we study the three-dimensional axisymmetric Navier-Stokes systemwith nonzero swirl. By establishing a new key inequality for the pair (wr, wθ),weget several Prodi-Serrin type regularity criteria based on the angular velocity,uθ.(Joint work with Professor Daoyuan Fang and Hui Chen)******************************************************************
Vanishing Viscosity Method for Non-identity ViscosityMatrix
Yi ZhouFudan University, [email protected]
We consider vanishing viscosity limit for systems of strictly hyperbolic conser-vation laws in one space dimension with nonidentity viscosity matrix.Under theassumption that A commutes with B and all the eigenvalue of B are positiveconstants, we prove that the parabolic regularization has a global smooth solu-tion which converges to the entropy weak solution of the hyperbolic conservationlaws provide the total variation of the initial data is sufficiently small.******************************************************************
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Some Recent Studies on the Generalized MHD andHall-MHD Systems
Yong ZhouShanghai University of Finance and Economics, China
The talk is mainly concerned with some recent studies on the generalized MHDand Hall-MHD systems. First, we will give a brief review of progress on well-posedness and regularity. Thenour recent works will be introduced. Finally,some open problems will be discussed.******************************************************************
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