international online conference onmath.sjtu.edu.cn/conference/2020npde/images/program book.pdf ·...
TRANSCRIPT
International Online Conference on
Nonlinear Evolutionary Partial Differential Equations:
Theories and Applications
(NEPDE 2020)
December 1-5, 2020
Shanghai Jiao Tong University (China)
Université Clermont Auvergne (France)
City University of Hong Kong (Hong Kong, China)
Table of Contents
Objectives………………………………..……………………………………….…………………………………………..1
Organizing Committee………..……………………………………….…………………………………………..1
Sponsors………………………………………………………………………………………………………………………2
Online Meeting Information………………………………..…………………………………………………..2
Conference Homepage……………………………………………………………………………………….......... 2
Contact……………………………………………………………………………………………………………………2
Useful Websites………….……………………………………………………………………………………………...2
List of Invited Participants………………………………………………………………………..3
Participants of the Youth Forum…………………………………………………………………………7
Talk Schedule based on Beijing Time…….……………………………...………………………………8
Comparison Table of Time Difference…………………………………………………………9
Schedule by Day based on Beijing Time………………………..…………..……………………….10
Abstracts………………………………………………………………………………………………………………15
2020 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
1
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, to
explore new research directions and topics, and to foster new collaborations and
connections. The main topics include:
Hyperbolic Problems
Parabolic and Elliptic Equations
Equations of Mixed Type
Conservation Laws
Euler Equations and Navier-Stokes Equations
Boltzmann Equation
Fluid Dynamics
Applications of PDEs
Other related topics in PDEs
Organizing Committee
Song Jiang
(Beijing Institute of Applied Physics and Computational Mathematics, China)
Congming Li
(Shanghai Jiao Tong University, China)
Tatsien Li
(Fudan University, China)
Yachun Li
(Shanghai Jiao Tong University, China)
Chengjie Liu
(Shanghai Jiao Tong University, China)
Yue-Jun Peng
(Université Clermont Auvergne, France)
Weike Wang
(Shanghai Jiao Tong University, China)
Ya-Guang Wang
(Shanghai Jiao Tong University, China)
Feng Xie
(Shanghai Jiao Tong University, China)
Tong Yang
(City University of Hong Kong, China)
2020 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
2
Sponsors
The organizing committee wishes to extend their thanks and appreciation to the
sponsors for their generous support:
School of Mathematical Sciences, Shanghai Jiao Tong University
Wu Wen-Tsun Center of Mathematical Sciences, Shanghai Jiao Tong University
National Natural Science Foundation of China
Network of International Centers of Education in China (国际化示范学院), Ministry
of Science and Technology & Ministry of Education
Institute of Natural Sciences, Shanghai Jiao Tong University
MOE Key Lab on Scientific and Engineering Computing
Shanghai Center for Applied Mathematics (SJTU center)
Online Meeting Information
The conference is to be held online through the Tencent VooV Meeting.
A. Tencent VooV Meeting Link: https://voovmeeting.com/s/lhW07m3Pmp7j
Room ID: 668 0535 3125; Password: 496534.
B. Other related links:
a) Download VooV Meeting: https://voovmeeting.com/download-center.html
b) An instruction of usage:
http://math.sjtu.edu.cn/conference/2020nPDE/images/An%20Instruction%20of
%20Using%20VOOV%20Meeting.pdf
Conference Homepage
http://math.sjtu.edu.cn/conference/2020nPDE
Contact
Yachun Li: [email protected]
Liang Zhao: [email protected]
Useful Websites
Shanghai Jiao Tong University (SJTU): www.sjtu.edu.cn
School of Mathematical Sciences, SJTU: www.math.sjtu.edu.cn Wu Wen-Tsun Center of Mathematical Sciences, SJTU: https://wucms.sjtu.edu.cn
Network of International Centers of Education in China: www.nice-math.sjtu.edu.cn
Institute of Natural Sciences, SJTU: https://ins.sjtu.edu.cn MOE Key Lab on Scientific and Engineering Computing: http://math.sjtu.edu.cn:9001
Shanghai Center for Applied Mathematics (SJTU center): http://shcam.sjtu.edu.cn
2020 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
3
List of Invited Participants
1. Myoungjean Bae (Pohang University of Science and Technology, Korea)
2. Leonid Berlyand (The Pennsylvania State University, USA)
3. Stefano Bianchini (Scuola Internazionale Superiore di Studi Avanzati, Italy)
4. Alberto Bressan (The Pennsylvania State University, USA)
5. Gui-Qiang G. Chen (University of Oxford, UK)
6. Hua Chen (Wuhan University, China)
7. Li Chen (Universität Mannheim, Germany)
8. Shijin Deng (Shanghai Jiao Tong University, China)
9. Yinbin Deng (Central China Normal University, China)
10. Renjun Duan (The Chinese University of Hong Kong, Hong Kong, China)
11. Beixiang Fang (Shanghai Jiao Tong University, China)
12. Eduard Feireisl (The Academy of Sciences of Czech Republic, Czech Republic)
13. Mikhail Feldman (University of Wisconsin-Madison, USA)
14. Hermano Frid (Instituto de Matemática Pura e Applicada-IMPA, Brazil)
15. David Gerard-Varet (Université de Paris, France)
16. Qilong Gu (Shanghai Jiao Tong University, China)
17. Graziano Guerra (Università degli Studi di Milano--Bicocca, Italy)
18. Lingbing He (Tsinghua University, China)
19. Feimin Huang (Chinese Academy of Sciences, China)
20. Sameer Iyer (Princeton University, USA)
21. Shi Jin (Shanghai Jiao Tong University, China)
2020 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
4
22. Qiangchang Ju (Beijing Institute of Applied Physics and Computational
Mathematics, China)
23. Stéphane Junca (Université Côte d'Azur, France)
24. Yoshiyuki Kagei (Tokyo Institute of Technology, Japan)
25. Zhen Lei (Fudan University, China)
26. Hailiang Li (Capital Normal University, China)
27. Jing Li (Chinese Academy of Sciences, China)
28. Tao Luo (City University of Hong Kong, Hong Kong, China)
29. Ming Mei (McGill University, Canada)
[email protected] [email protected]
30. Chunlai Mu (Chongqing University, China)
31. Toan T. Nguyen (The Pennsylvania State University, USA)
32. Shinya Nishibata (Tokyo Institute of Technology, Japan)
33. Ronghua Pan (Georgia Institute of Technology, USA)
34. Shuangjie Peng (Central China Normal University, China)
35. Yuming Qin (Donghua University, China)
36. Reinhard Racke (University of Konstanz, Germany)
37. Michael Reissig (Technische Universität Bergakademie Freiberg, Germany)
38. Paolo Secchi (University of Brescia, Italy)
39. Denis Serre (École Normale Supérieure de Lyon, France)
40. Henrik Shahgholian (The Royal Institute of Technology-KTH, Sweden)
41. Wen Shen (The Pennsylvania State University, USA)
42. Wancheng Sheng (Shanghai University, China)
2020 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
5
43. Zhong Tan (Xiamen University, China)
44. Youshan Tao (Shanghai Jiao Tong University, China)
45. Chunpeng Wang (Jilin University, China)
46. Dehua Wang (University of Pittsburgh, USA)
47. Fang Wang (Shanghai Jiao Tong University, China)
48. Fei Wang (Shanghai Jiao Tong University, China)
49. Haitao Wang (Shanghai Jiao Tong University, China)
50. Shu Wang (Beijing University of Technology, China)
51. Xiaoming Wang (Southern University of Science and Technology, China)
52. Xiao-Ping Wang (Hong Kong University of Science and Technology, Hong Kong,
China)
53. Zhi-an Wang (The Hong Kong Polytechnic University, Hong Kong, China)
54. Huanyao Wen (South China University of Technology, China)
55. Mark Williams (University of North Carolina-Chapel Hill, USA)
56. Wei Xiang (City University of Hong Kong, Hong Kong, China)
57. Chunjing Xie (Shanghai Jiao Tong University, China)
58. Feng Xie (Shanghai Jiao Tong University, China)
59. Zhouping Xin (The Chinese University of Hong Kong, Hong Kong, China)
60. Chaojiang Xu (Nanjing University of Aeronautics and Astronautics, China)
[email protected] [email protected]
61. Jiang Xu (Nanjing University of Aeronautics and Astronautics, China)
62. Xiaoping Yang (Nanjing University, China)
[email protected] [email protected]
63. Xiongfeng Yang (Shanghai Jiao Tong University, China)
2020 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
6
64. Zheng-an Yao (Sun Yat-sen University, China)
65. Huicheng Yin (Nanjing Normal University, China)
[email protected] [email protected]
66. Liqun Zhang (Chinese Academy of Sciences, China)
67. Ping Zhang (Chinese Academy of Sciences, China)
68. Zhifei Zhang (Peking University, China)
69. Zhu Zhang (City University of Hong Kong, Hong Kong, China)
70. Huijiang Zhao (Wuhan University, China)
71. Yi Zhou (Fudan University, China)
72. Changjiang Zhu (South China University of Technology, China)
73. Peicheng Zhu (Shanghai University, China)
74. Shengguo Zhu (Shanghai Jiao Tong University, China)
2020 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
7
Participants of the Youth Forum
1. Yue Cao (Shanghai Jiao Tong University, China)
2. Wenhui Chen (Shanghai Jiao Tong University, China)
3. Hao Li (Shanghai Jiao Tong University, China)
4. Yuanyuan Lian (Shanghai Jiao Tong University, China)
5. Chenkai Liu (Shanghai Jiao Tong University, China)
6. Lei Ma (Shanghai Jiao Tong University, China)
7. Mohamad Rachid (Université de Nantes, France)
8. Zhaoyang Shang (Shanghai Jiao Tong University, China)
9. Binbin Shi (Shanghai Jiao Tong University, China)
10. Srđan Trifunović (University of Novi Sad, Serbia)
11. Chenmu Wang (Shanghai Jiao Tong University, China)
12. Lidan Wang (Shanghai Jiao Tong University, China)
13. Qianyun Wang (Shanghai Jiao Tong University, China)
14. Shaodong Wang (Shanghai Jiao Tong University, China)
15. Xiang Wang (Shanghai Jiao Tong University, China)
16. Yucheng Wang (Shanghai Jiao Tong University, China)
17. Zirong Zeng (Shanghai Jiao Tong University, China)
18. Liang Zhao (Shanghai Jiao Tong University, China)
19. Huihuang Zhou (Shanghai Jiao Tong University, China)
2020 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
Tencent VooV Meeting Link: https://voovmeeting.com/s/lhW07m3Pmp7j ID: 668 0535 3125; Password: 496534
Myoungjean Bae Leonid Berlyand Dehua Wang Ming Mei Srđan Trifunović
Chair: Congming Li Chair: Fang Wang Chair: Chunpeng Wang Chair: Hua Chen Yuanyuan Lian
Yoshiyuki Kagei Alberto Bressan Toan T. Nguyen Mark Williams Chenkai Liu
Chair: Chunjing Xie Chair: Yachun Li Chair: Feng Xie Chair: Liqun Zhang Lei Ma
Ping Zhang Sameer Iyer Ronghua Pan Wen Shen Zhaoyang Shang
Chair: Weike Wang Chair: Shijin Deng Chair: Shu Wang Chair: Chaojiang Xu Binbin Shi
Xiao-Ping Wang Mikhail Feldman Shinya Nishibata Zhu Zhang Chenmu Wang
Chair: Tong Yang Chair: Xiaoming Wang Chair: Feimin Huang Chair: Fei Wang Lidan Wang
Tao Luo Yi Zhou Zhouping Xin Huanyao Wen Qianyun Wang
Chair: Haitao Wang Chair: Zhen Lei Chair: Song Jiang Chair: Zheng-an Yao Shaodong Wang
Renjun Duan Zhi-an Wang Lingbing He Peicheng Zhu Xiang Wang
Chair: Chengjie Liu Chair: Youshan Tao Chair: Xiongfeng Yang Chair: Qilong Gu Yucheng Wang
Henrik Shahgholian Wei Xiang Eduard Feireisl Jiang Xu Zirong Zeng
Chair: Shuangjie Peng Chair: Beixiang Fang Chair: Ya-Guang Wang Chair: Wancheng Sheng Liang Zhao
Stefano Bianchini Stéphane Junca Paolo Secchi Qiangchang Ju Huihuang Zhou
Chair: Shi Jin Chair: Yue-Jun Peng Chair: Huicheng Yin Chair: Zhong Tan Mohamad Rachid
Hermano Frid Feng Xie Chunjing Xie Li Chen
Chair: Zhifei Zhang Chair: Changjiang Zhu Chair: Jing Li Chair: Yinbin Deng
Graziano Guerra Michael Reissig Reinhard Racke Half hour break
Chair: Shengguo Zhu Chair: Chunlai Mu Chair: Yuming Qin Yue Cao
David Gerard-Varet Denis Serre Gui-Qiang G. Chen Wenhui Chen
Chair: Xiaoping Yang Chair: Huijiang Zhao Chair: Hailiang Li Hao Li
Asia Brazil Europe The Chinese Mainland Youth Forum
21:00-22:00
7
8
9
10
20:00-21:00
19:00-20:00
Tea Break
Shanghai Jiao Tong University (China), Université Clermont Auvergne (France), City University of Hong Kong (Hong Kong, China)
Dec.5 (Saturday)
Tea Break
2
3
4
6
Nonlinear Evolutionary Partial Differential Equations (NEPDE 2020)
Dec.4 (Friday)Time Period
1
North America
Time Zone: GMT+8 (Beijing Time)
Dec.1 (Tuesday) Dec.2 (Wednesday) Dec.3 (Thursday)
11
08:00-09:00
09:00-10:00
10:00-11:00
11:00-12:00
14:00-15:00
15:00-16:00
16:00-17:00
17:00-18:00
12
Remark: The colors represent different regions of speakers.
8
2020 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications 9
TimeZone
(GMT+X)Time
Timedifference
-6 Central Standard Time(USA) -14 18:00 19:00 20:00 21:00 22:00 23:00 0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00
-5Eastern Standard Time(USA),Canada
-13 19:00 20:00 21:00 22:00 23:00 0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00
-3 Brazil Rio Time -10 22:00 23:00 0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00
+0 UK Time -8 0:00 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00
+1 Central European Time -7 1:00 2:00 3:00 4:00 5:00 6:00 7:00 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00
+9 Asia Time (Japan, Korea) +1 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00 23:00
+8 Beijing Time 0 8:00 9:00 10:00 11:00 12:00 13:00 14:00 15:00 16:00 17:00 18:00 19:00 20:00 21:00 22:00
A Comparison Table of Time difference (NEPDE 2020)
Conference Time
2020 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
10
Schedule by Day based on Beijing Time
Day 1: Dec. 1 (Tuesday) Morning Session
08:00-09:00
Myoungjean Bae (Chair: Congming Li)
Detached shocks past a blunt body
09:00-10:00
Yoshiyuki Kagei (Chair: Chunjing Xie)
Hopf bifurcation in the artificial compressible system for doubly diffusive
convection
10:00-11:00
Ping Zhang (Chair: Weike Wang)
Global existence and decay of solutions to Prandtl system with small
analytic and Gevrey data
11:00-12:00
Xiao-Ping Wang (Chair: Tong Yang)
Threshold Dynamics Method and Applications
Afternoon Session
14:00-15:00
Tao Luo (Chair: Haitao Wang)
On some fluids/MHD free boundaries
15:00-16:00
Renjun Duan (Chair: Chengjie Liu)
The Boltzmann equation with large-amplitude initial data and specular
reflection boundary condition
16:00-17:00
Henrik Shahgholian (Chair: Shuangjie Peng)
Global solutions to the obstacle problem
17:00-18:00
Stefano Bianchini (Chair: Shi Jin)
On the sticky particle solutions to the multi-dimensional pressureless
Euler equations
Evening Session
19:00-20:00
Hermano Frid (Chair: Zhifei Zhang)
The strong trace property and the Neumann problem for stochastic
conservation laws
20:00-21:00
Graziano Guerra (Chair: Shengguo Zhu)
Vanishing viscosity solutions for conservation laws with discontinuous
fluxes
21:00-22:00
David Gerard-Varet (Chair: Xiaoping Yang)
On the stability of boundary layers with concave profile
2020 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
11
Day 2: Dec. 2 (Wednesday) Morning Session
08:00-09:00
Leonid Berlyand (Chair: Fang Wang)
Emergence of traveling waves and their stability analysis in a free
boundary model of cell motility
09:00-10:00
Alberto Bressan (Chair: Yachun Li)
A posteriori error estimates for numerical solutions to hyperbolic
conservation laws
10:00-11:00
Sameer Iyer (Chair: Shijin Deng)
Global in x stability of Prandtl’s boundary layer for 2D, stationary
Navier-Stokes flows
11:00-12:00
Mikhail Feldman (Chair: Xiaoming Wang)
Weak-strong uniqueness and stability for the semigeostrophic system
Afternoon Session
14:00-15:00
Yi Zhou (Chair: Zhen Lei)
Global regularity for Einstein-Klein-Gordon system with U (1) × R
isometry group
15:00-16:00
Zhi-an Wang (Chair: Youshan Tao)
Phase transition solutions to a hyperbolic-parabolic system modeling
vascular networks
16:00-17:00
Wei Xiang (Chair: Beixiang Fang)
Convexity and uniqueness of the regular shock reflection for the
potential flow
17:00-18:00
Stephane Junca (Chair: Yue-Jun Peng)
Existence in fractional BV spaces for 2x2 strictly hyperbolic systems of
conservations laws
Evening Session
19:00-20:00
Feng Xie (Chair: Changjiang Zhu)
Conducting fluids with a moving physical boundary
20:00-21:00
Michael Reissig (Chair: Chunlai Mu)
Global (in time) existence versus blow-up phenomena
21:00-22:00
Denis Serre (Chair: Huijiang Zhao)
Hard spheres dynamics: estimating the collisions through compensated
integrability
2020 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
12
Day 3: Dec. 3 (Thursday) Morning Session
08:00-09:00
Dehua Wang (Chair: Chunpeng Wang)
Euler equations, transonic flows and isometric embeddings
09:00-10:00
Toan T. Nguyen (Chair: Feng Xie)
The instablility of boundary layers
10:00-11:00
Ronghua Pan (Chair: Shu Wang)
Isentropic approximation
11:00-12:00
Shinya Nishibata (Chair: Feimin Huang)
Existence and asymptotic stability of a stationary wave to a symmetric
hyperbolic-parabolic system of conservation laws
Afternoon Session
14:00-15:00
Zhouping Xin (Chair: Song Jiang)
On subsonic flows around a profile with a vortex line
15:00-16:00
Lingbing He (Chair: Xiongfeng Yang)
A new monotonicity formula for the spatially homogeneous Landau
equation with Coulomb potential and its applications
16:00-17:00
Eduard Feireisl (Chair: Ya-Guang Wang)
On the density of “wild” initial data for the compressible Euler system
17:00-18:00
Paolo Secchi (Chair: Huicheng Yin)
Weakly nonlinear surface waves on the plasma-vacuum interface
Evening Session
19:00-20:00
Chunjing Xie (Chair: Jing Li)
Analysis on steady compressible jet flows with nonzero vorticity
20:00-21:00
Reinhard Racke (Chair: Yuming Qin)
Hyperbolic compressible Navier-Stokes equation
21:00-22:00
Gui-Qiang G. Chen (Chair: Hailiang Li)
Cavitation and Concentration in Entropy Solutions to the Euler and
Related NEPDEs
2020 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
13
Day.4: Dec. 4 (Friday) Morning Session
08:00-09:00
Ming Mei (Chair: Hua Chen)
Optimal decay rates of 3D compressible Euler equations with
time-dependent damping
09:00-10:00
Mark Williams (Chair: Liqun Zhang)
Hyperbolic boundary problems with large oscillatory lower order terms:
multiple amplification
10:00-11:00
Wen Shen (Chair: Chaojiang Xu)
Nonlocal models for traffic flow
11:00-12:00
Zhu Zhang (Chair: Fei Wang)
Some recent studies on steady MHD boundary layers
Afternoon Session
14:00-15:00
Huanyao Wen (Chair: Zheng-an Yao)
Global well-posedness and time-decay estimates for compressible
Navier-Stokes equations with reaction diffusion
15:00-16:00
Peicheng Zhu (Chair: Qilong Gu)
New phase-field models for martensitic phase transformations with
applications to MGI
16:00-17:00
Jiang Xu (Chair: Wancheng Sheng)
The dissipative structure of compressible Navier-Stokes-Korteweg
equations and its applications
17:00-18:00
Qiangchang Ju (Chair: Zhong Tan)
Singular limit for equatorial shallow water dynamics
Evening Session
19:00-20:00
Li Chen (Chair: Yinbin Deng)
Combined mean-field and semiclassical limits of large fermionic systems
20:30-21:00
Yue Cao
Local strong solutions to the full compressible Navier-Stokes system with
temperature-dependent viscosity and heat conductivity
21:00-21:30
Wenhui Chen
Blow-up of solutions to Nakao’s problem via an iteration argument
21:30-22:00
Hao Li
Global strong solutions to the two-dimensional full compressible
Navier-Stokes equations with large viscosity
2020 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
14
Day 5: Dec. 5 (Saturday)
08:00-08:30 Srđan Trifunovic
On the interaction between compressible viscous fluids and plates
08:30-09:00
Yuanyuan Lian
Boundary Holder regularity for fully nonlinear elliptic equations on Reifenberg flat
domains
09:00-09:30 Chenkai Liu
On Dirichlet problem for the fractional Laplacian
09:30-10:00
Lei Ma
Low Mach number limit and far field convergence rates of potential flows in
multi-dimensional nozzles with an obstacle inside
10:00-10:30
Zhaoyang Shang
Global existence of classical solutions to the two-dimensional compressible
Boussinesq equations in a square domain
10:30-11:00
Binbin Shi
Suppression of blow up by mixing in generalized Keller-Segel system with fractional
dissipation
11:00-11:30
Chenmu Wang
Partial exact boundary synchronization and partial approximate boundary
synchronization for a coupled system of wave equations
11:30-12:00
Lidan Wang
Classification of positive solutions for fully nonlinear elliptic equations in unbounded
cylinder
14:00-14:30 Qianyun Wang
The closed range property for the d-bar operator
14:30-15:00 Shaodong Wang
On the construction of blowing-up solutions to some nonlinear elliptic equations
15:00-15:30 Xiang Wang
On the back flow of the mixed Prandtl-Hartmann boundary layer problem
15:30-16:00
Yucheng Wang
Global existence and large time behavior for the chemotaxis–shallow water system in
a bounded domain
16:00-16:30 Zirong Zeng
Mild solutions of the stochastic MHD equations driven by fractional Brownian motions
16:30-17:00
Liang Zhao
The rigorous derivation of unipolar Euler-Maxwell system for electrons from bipolar
Euler-Maxwell system by infinity-ion-mass limit
17:00-17:30 Huihuang Zhou
On the compactness of conformally compact Einstein manifold
17:30-18:00 Mohamad Rachid
Incompressible Navier-Stokes-Fourier limit from the Landau equation
2020 International Conference on Nonlinear Evolutionary Partial Differential Equations--Theories and Applications
15
Abstracts (Invited Speakers)
Detached shocks past a blunt bodyMyoungjean Bae
Pohang University of Science and Technology, Korea
The shock polar analysis shows that if a weak solution of steady Euler system for inviscid com-pressible flow has a shock past a blunt body, then the shock cannot be attached to the blunt body.This observation naturally raises a question on the existence of a detached shock solution past a bluntbody. In this talk, I will present a recent result on the existence of detached shocks past a blunt bodywith a asymptotic state at far field. If time permits, I will also discuss on further open questions ondetached shocks. This talk is based on a joint work with Wei Xiang(CUHK).
Emergence of traveling waves and their stability analysis in a freeboundary model of cell motility
Leonid Berlyand
The Pennsylvania State University, USA
We introduce a novel two-dimensional Hele-Shaw type free boundary model for motility of eukary-otic cells on substrates. The key ingredients of this model are the Darcy law for overdamped motion ofthe cytoskeleton gel (active gel) coupled with advection-diffusion equation for myosin density leadingto elliptic-parabolic Keller-Segel system. This system is supplemented with HeleShaw type boundaryconditions: Young-Laplace equation for pressure and continuity of velocities. We first show that ra-dially symmetric stationary solutions become unstable and bifurcate to traveling wave solutions at acritical value of the total myosin mass. Next we perform linear stability analysis of these travelingwave solutions and identify the type of bifurcation (sub- or supercritical). Our study sheds light onthe mathematics underlying instability/stability transitions in this model. Specifically, we show thatthese transitions typically occur via generalized eigenvectors of the linearized operator and we deriveda simple explicit formula for the eigenvalue that determines the stability of traveling waves. The gener-alized eigenvector appears due to non self-adjointness of this operator, which is the signature of activematter PDE models. Finally we present the moist recent result on bistability. These is a joint workwith V. Rybalko (ILTPE, Ukraine). If time permits, we will discuss recent work in progress on freeboundary models of tissue growth (joint with J. Casademunt, et al) and numerics (with A. Safsten).
1
On the sticky particle solutions to the multi-dimensional pressurelessEuler equations
Stefano Bianchini
Scuola Internazionale Superiore di Studi Avanzati, Italy
In this paper we consider the multi-dimensional pressureless Euler system and we tackle the problemof existence and uniqueness of sticky particle solutions for general measure-type initial data. Althoughexplicit counterexamples to both existence and uniqueness are known since [Bressan-Nguyen, 2014],the problem of whether one can still find sticky particle solutions for a large set of data and of howone can select them was up to our knowledge still completely open.
In this paper we prove that for a comeager set of initial data in the weak topology the pressurelessEuler system admits a unique sticky particle solution given by a free flow where trajectories are disjointstraight lines.
Indeed, such an existence and uniqueness result holds for a broader class of solutions decreasingtheir kinetic energy, which we call dissipative solutions, and which turns out to be the compact weakclosure of the classical sticky particle solutions. Therefore any scheme for which the energy is l.s.c.and is dissipated will converge, for a comeager set of data, to our solution, i.e. the free flow.
A posteriori error estimates for numerical solutions to hyperbolicconservation laws
Alberto Bressan
The Pennsylvania State University, USA
For general n× n hyperbolic systems of conservation laws in one space dimension, it is well knownthat the Cauchy problem has a unique entropy-weak solution, depending continuously on the initialdata. Assuming small total variation, a priori estimates on the L1 distance between an approximatesolution and the exact solution have been obtained in connection with (i) front tracking approximations,(ii) the Glimm scheme, and (iii) vanishing viscosity approximations. However, no a priori estimate isyet known for approximate solutions obtained by fully discrete schemes, such as the Lax-Friedrichs orthe Godunov scheme.
In this talk I shall explain the key obstruction toward a priori error bounds for such discreteschemes. Taking a different point of view, I will present some recent results on a posteriori errorestimates. These are achieved by a ”post-processing algorithm” that checks the total variation of thenumerically computed solution, and computes its oscillation on suitable subdomains.
This is a joint work with Maria Teresa Chiri and Wen Shen.
2
Cavitation and Concentration in Entropy Solutions to the Euler andRelated NEPDEs
Gui-Qiang G. Chen
University of Oxford, UK
In this talk, we will discuss the intrinsic phenomena of cavitation/decavitation and concentra-tion/deconcentration in entropy solutions to the compressible Euler equations and related NEPDEs,which are fundamental to understand the well-posedness and solution behaviors of nonlinear hyperbolicsystems of conservation laws. We will start with our discussion of the formation process of cavitationand concentration in the entropy solutions of the one-dimensional isentropic Euler equations withrespect to the initial data and the vanishing pressure limit. Then we will analyze a longstandingfundamental problem in fluid dynamics: Does the concentration occur generically so that the densitydevelops into a Dirac measure at the origin generically in spherically symmetric entropy solutionsof the multi-dimensional compressible Euler equations? We will report our most recent results andapproaches developed for solving this longstanding open problem for the Euler equations and relatedNEPDEs, and will discuss its close connections with entropy methods and the theory of divergence-measure fields. Further related topics, perspectives, and open problems in this direction will also beaddressed.
Combined mean-field and semiclassical limits of large fermionicsystems
Li Chen
Universität Mannheim, Germany
I will take about the combined mean field and semiclassical limits of the time dependent Schrödingerequation for large spinless fermions with the semiclassical scale N1/3 in three dimensions. By usingthe Husimi measure defined by coherent states, we rewrite the Schrödinger equation into a BBGKYtype of hierarchy for the k particle Husimi measure. Further estimates are derived to obtain the weakcompactness of the Husimi measure, and in addition uniform estimates for the remainder terms in thehierarchy are derived in order to show that in the semiclassical regime the weak limit of the Husimimeasure is exactly the solution of the Vlasov equation. This is a joint work with Jinyeop Lee andMatthew Liew.
3
The Boltzmann equation with large-amplitude initial data andspecular reflection boundary condition
Renjun Duan
The Chinese University of Hong Kong, Hong Kong, China
For the Boltzmann equation with cutoff hard potentials, we construct the unique global solutionconverging with an exponential rate in large time to global Maxwellians not only for the specular re-flection boundary condition with the bounded convex C3 domain but also for a class of large amplitudeinitial data where the L∞ norm with a suitable velocity weight can be arbitrarily large but the relativeentropy need to be small. A key point in the proof is to introduce a delicate nonlinear iterative processof estimating the gain term basing on the triple Duhamel iteration along the linearized dynamics. Thiswork is joint with Gyounghun Ko and Donghyun Lee.
On the density of “wild” initial data for the compressible Euler systemEduard Feireisl
The Academy of Sciences of Czech Republic, Czech Republic
We consider a class of “wild” initial data to the compressible Euler system that give rise to infinitelymany admissible weak solutions via the method of convex integration. We identify the closure of thisclass in the natural L1−topology and show that its complement is rather large, specifically it is anopen dense set.
Weak-strong uniqueness and stability for the semigeostrophic systemMikhail Feldman
University of Wisconsin-Madison, USA
The semigeostrophic (SG) system is a model of large scale atmosphere/ocean flows. Solutions ofthis system are expected to contain singularities corresponding to the atmospheric fronts, and needto be understood in the appropriate weak sense. We will survey the results on existence of weaksolutions. Then we will describe recent results on weak-strong uniqueness for SG system, and onconvergence of smooth solutions of incompressible Euler system with Coriolis force to a sufficientlyregular solution of SG system in 2D and 3D. In both results main assumptions on the strong solutionare the boundedness of the velocity field and the uniform convexity of the Legendre-Fenchel transformof the modified pressure. Both results are obtained by the relative entropy techniques.
This talk is based on joint works with M. Cullen and A. Tudorascu.
4
The strong trace property and the Neumann problem forstochastic conservation laws
Hermano Frid
Instituto de Matemática Pura e Aplicada-IMPA, Brazil
We present some recent well-posedness results on initial-boundary value problems for stochasticparabolic-hyperbolic equations. In the first part of the talk, we analyze the Neumann problem forstochastic conservation laws. In the second part, we analyze a mixed type initial-boundary valueproblem for a stochastic degenerate parabolic-hyperbolic equation. In each of these problems, a newstochastic strong trace theorem is presented which plays a decisive role in the proof of the uniquenessof the kinetic solutions. This is a joint work with Yachun Li, Daniel Marroquin, João Nariyoshiand Zirong Zeng.
On the stability of boundary layers with concave profileDavid Gerard-Varet
Université de Paris, France
I will present a joint work with Y. Maekawa and N. Masmoudi, in which we show the stabilityof boundary layer expansions for Navier-Stokes equations in a half plane, on a time interval that isuniform in the vanishing viscosity limit. This stability is obtained under a mild concavity assumptionon the boundary layer profile and for perturbations with Gevrey regularity. Optimality of this resultwill be explained.
5
Vanishing viscosity solutions for conservation laws with discontinuousfluxes
Graziano Guerra
Università degli Studi di Milano–Bicocca, Italy
Scalar conservation laws with fluxes that depend on the space–time variables in a discontinuousway arise in many applications where the conservation laws describe physical models in rough nonhomogeneous media. For instance, traffic flows with rough road conditions or polymer flooding inporous media. We are interested in solutions to this type of equations obtained by vanishing viscosityapproximations. We describe the non uniqueness of solutions to the Riemann problem when the fluxis independent of time and has a single discontinuity in space at the origin. The unique solutionobtained by the vanishing viscosity limit is singled out. Then we consider the Cauchy problem andshow that the Crandall Liggett theory of nonlinear semigroups provides a very elegant framework toprove existence and uniqueness to the vanishing viscosity limit. We finally show how this result can beused to generalize existence and uniqueness of viscosity solutions to equations with fluxes which dependon both the space and the time variables in a very discontinuous way. The uniqueness is proved througha comparison principle for the corresponding Hamilton-Jacobi equations and the existence through acompensated compactness argument.
A new monotonicity formula for the spatially homogeneous Landauequation with Coulomb potential and its applications
Lingbing He
Tsinghua University, China
In this talk, we describe a time-dependent functional involving the relative entropy and the H1 semi-norm, which decreases along solutions to the spatially homogeneous Landau equation with Coulombpotential. The study of this monotone functionial sheds light on the competition between the dis-sipation and the nonlinearity for this equation. It enables to obtain new results concerning regular-ity/blowup issues for the Landau equation with Coulomb potential. The talk is based on the jointwork with L.Desvillettes and J.-C.Jiang.
6
Global in x stability of Prandtl’s boundary layer for 2D, stationaryNavier-Stokes flows
Sameer Iyer
Princeton University, USA
In this talk I will discuss a recent work which proves stability of Prandtl’s boundary layer in thevanishing viscosity limit. The result is an asymptotic stability result of the background profile in twosenses: asymptotic as the viscosity tends to zero and asymptotic as x (which acts a time variable) goesto infinity. In particular, this confirms the lack of the ”boundary layer separation” in certain regimeswhich have been predicted to be stable. This is joint work w. Nader Masmoudi (Courant Institute,NYU).
Singular limit for equatorial shallow water dynamicsQiangchang Ju
Beijing Institute of Applied Physics and Computational Mathematics, China
We study the singular limit for equatorial shallow water equations at low Froude number forming asymmetric hyperbolic system with large variable coefficient terms. Based on the convergence result ofDurtrifoy, Majda and Schochet [Comm. Pure Appl. Math(2009)], we further obtain the convergencerate estimates of the solutions. This is a recent joint work with Jiang, Song and Xu, Xin.
Existence in fractional BV spaces for 2x2 strictly hyperbolic systemsof conservations laws
Stéphane Junca
Université Côte d’Azur, France
For hyperbolic systems of one-dimensional conservation laws, the theory of existence of global weakenropy solutions for the initial value problem is generally performed for small initial data in BV or,rarely, in L∞. In this presentation, the intermediate spaces BV s, 0 < s < 1, are used, BV = BV 1 andL∞ = BV 0. The 2×2 strictly hyperbolic systems with genuinely nonlinear or lineraly degenerate fieldsare considered, so there are three cases. The first case, a full genuinely nonlinear system, is alreadyknown since Glimm-Lax 1970 and Bianchini-Colombo-Monti 2010, for small L∞ initial data there isa smoothing in BV like for the scalar case with an uniformly convex flux, Lax and Oleinik 1957. Forthe second case, a full linearly degenerate system, the existence holds in any BV s. For the third case,the main part of the talk, one field is genuinely nonlinear and the other one is linearly degnerate, acritical fractional regularity s = 1/3 appears. Optimality of s = 1/3 is proven on a triangular system.
7
Hopf bifurcation in the artificial compressible system for doublydiffusive convection
Yoshiyuki Kagei
Tokyo Insitute of Technology, Japan
The 2-dimensional doubly diffusive convection problem is considered for the artificial compressiblesystem. The incompressible Oberbeck-Boussinesq system is obtained as a singular limit with theartificial Mach number ε → 0. It is known for the incompressible system that if the bifurcationparameter increases beyond a certain critical value, then the motionless state becomes unstable and atime periodic flow bifurcates. In this talk, we show that there also exists a bifurcating time periodicsolution for the artificial compressible system when the artificial Mach number ε is sufficiently small.The convergence of the bifurcating branch for the artificial compressible system as ε → 0 is alsoconsindered. This talk is based on a joint work with Prof. C.-H. Hsia (National Taiwan Univ.), Prof.T. Nishida (Kyoto Univ.) and Prof. Y. Teramoto (Okayama Univ.).
On some fluids/MHD free boundariesTao Luo
City University of Hong Kong, Hong Kong, China
In this talk, I will first discuss the estimates for a free boundary problem of highly subsonic flowwith heat conductivity. Those estimates including the Sobolev estimates of fluid variables and somegeometric quantities on free surfaces. An interesting feature of this problem is that it loses one morederivatives than that for the incompressible or isentropic Euler equations. This result is joint withHuihui Zeng. If time allows, I will also discuss a problem of ideal incompressible MHD with closed freesurfaces, with emphasize on the Taylor sign condition to the ill/well-posedness, based on joint workswith Changchun Hao.
8
Optimal decay rates of 3D compressible Euler equations withtime-dependent damping
Ming Mei
Champlain College Saint-Lambert, McGill University, Canada
In this talk, we consider the multi-dimensional compressible Euler equations with time-dependentdamping of the form − µ
(1+t)λρu in Rn, where n ≥ 2, µ > 0, and λ ∈ [−1, 1). When λ > 0 (
λ < 0), the damping effect time-asymptotically gets weaker (stronger), which is called under-damping(over damping). We show the optimal decay estimates of the solutions in the under-damping andover-damping cases, respectively, and see how the under-damping effect influences the structure ofthe Euler system. The time-dependent damping affects essentially the structure of solutions to Eulerequations. Different from the traditional view that the stronger damping usually makes the solutionsdecaying faster, here we recognize that the weaker damping with 0 ≤ λ < 1 enhances the faster decayfor the solutions, and the effect of the stronger damping with −1 ≤ λ < 0 reduces the decay of thesolutions to be slower. The approach adopted for proof is the technical Fourier analysis and Greenfunction method.
This is a joint work with Shanming Ji.
The instability of boundary layersToan T. Nguyen
The Pennsylvania State University, USA
The talk is to overview recent developments on the classical boundary layer theory, including theanalysis of Orr-Sommerfeld equations and the resolvent for Navier-Stokes in the small viscosity limit.This is a joint work with E. Grenier (ENS Lyon).
Existence and asymptotic stability of a stationary waveto a symmetric hyperbolic-parabolic system of conservation laws
Shinya Nishibata
Tokyo Institute of Technology, Japan
In the present talk, we discuss an existence of a stationary wave and its large time behavior toa coupled system of viscous and inviscid conservation laws. We, mainly, talk about an asymptoticstability of the stationary wave under the assumption, the existence of an entropy function. Thiscondition allows us to transform the original system to a normal form of symmetric hyperbolic-parabolicsystems. In asymptotic analysis, we derive an a priori estimate by an energy method. In order toderive the basic estimate, we make use of an energy form, which is obtained by substituting a smoothapproximation of the stationary wave in the entropy function. The symmetric system is utilized inderiving the higher estimates of the derivatives of solutions. In this procedure, we use a stabilitycondition at spatial far field.
9
Isentropic approximationRonghua Pan
Georgia Institute of Technology, USA
In the study of compressible flows, the isentropic model was often used to replace the more com-plicated full system when the entropy is near a constant. This is based on the expectation that thecorresponding isentropic model is a good approximation to the full system when the entropy is suffi-ciently close to the constant. We will discuss the mathematical justification of isentropic approximationin Euler flows and in Navier-Stokes-Fourier flows. This is based on the joint work with Y. Chen, J.Jia, and L. Tong.
Hyperbolic compressible Navier-Stokes equationReinhard Racke
University of Konstanz, Germany
We consider the non-isentropic compressible Navier-Stokes equations with hyperbolic heat conduc-tion and a law for the stress tensor which is modified correspondingly by Maxwell’s law. These tworelaxations, turning the whole system into a hyperbolic one, are not only treated simultaneously, butare also considered in a version having Galilean invariance. For this more complicated relaxed system,the global well-posedness is proved for small data. Moreover, for vanishing relaxation parameters thesolutions are shown to converge to solutions of the classical system.
Global (in time) existence versus blow-up phenomenaMichael Reissig
Technische Universität Bergakademie Freiberg, Germany
In this talk we will discuss the Cauchy problem for semi-linear evolution models with source non-linearities of power type. The source nonlinearity allows, in general, the proof of global (in time)existence results for small data only. We discuss the question for critical exponents dividing the rangeof admissible exponents into a subset allows global (in time) existence results and a subset which im-plies blow-up phenomena (even) for small data. In the lecture we introduce recent results and explaindifferent methods to attack different evolution models. At the end of the talk we propose some openproblems.
10
Weakly nonlinear surface waves on the plasma-vacuum interfacePaolo Secchi
University of Brescia, Italy
In this talk we consider the free boundary problem for a plasma-vacuum interface in ideal incom-pressible magnetohydrodynamics. Unlike the classical statement, where the vacuum magnetic fieldobeys the div-curl system of pre-Maxwell dynamics, we do not neglect the displacement current inthe vacuum region and consider the Maxwell equations for electric and magnetic fields. Our aim is toconstruct weakly nonlinear, highly oscillating solutions to this plasma-vacuum interface problem.
Under a necessary and sufficient stability condition for a piecewise constant background state,we construct approximate solutions at any arbitrarily large order of accuracy to the free boundaryproblem in three space dimensions when the initial discontinuity displays high frequency oscillations.As evidenced in earlier works, high frequency oscillations of the plasma-vacuum interface solutiongive rise to Ôsurface wavesÕ on either side of the interface. Such waves decay exponentially in thenormal direction to the interface and, in the weakly nonlinear regime that we consider here, theirleading amplitude is governed by a nonlocal Hamilton-Jacobi type equation, as for Rayleigh waves inelastodynamics and current-vortex sheets in MHD.
This is a joint work with Yuan Yuan (CAMIS, South China Normal Univ.).
Hard spheres dynamics: estimatingthe collisions through compensated integrability
Denis Serre
École Normale Supérieure de Lyon, France
We consider N >> 1 hard spheres moving in the open space Rn (typically, n = 2 or 3). Thedynamics is completely described by binary collisions.
It has been known since 1975 (R. K. Alexander) that the Cauchy problem is uniquely solvable forgeneric initial data. In 1970, Ya. Sinai asked whether the collisions are finitely many as t ∈ (0,+∞).A positive answer was given in 1979 (L. N. Vaserstein, see also R. Illner 1989/90).
The only known upper bound of the number of collisions (Burago & al., 1998) is way too large tobe relevant. On the opposite side, some initial configurations yield exponentially many (in terms ofN) collisions.
We show here that at most O(N2) collisions are significant, in terms of the exchange of momentumbetween the colliding particles.
The proof involves an extension of our recent theory of Compensated Integrability for divergence-freepositive symmetric tensors. The dynamics is described in terms of such a tensor, in which we need tointroduce virtual particles called collitons. This tensor is rather singular (its support being a graph),so Compensated Integrability does not apply directly and we need an adaptation. We thus introducethe notion of determinantal masses of such a tensor at vertices and we prove a that CompensatedIntegrability incorporate these quantities.
11
Global solutions to the obstacle problemHenrik Shahgholian
The Royal Institute of Technology-KTH, Sweden
That ellipsoidal shells do not exert gravitational force inside the cavity of the shell was known toNewton, Laplace, and Ivory. In early 30’s P. Dive proved the inverse of this theorem. In this talk,I shall recall the (partially geometric) proof of this fact and then extend this result to unboundeddomains.
Since ellipsoids, and any limit of a sequence of ellipsoids, are the so-called coincidence sets for theobstacle problem, there is a close link between the ellipsoidal potential theory and global solutions tothe obstacle problem.
In this talk we present a complete classification (in terms of limit domains of ellipsoids) for globalsolutions to the obstacle problem in dimensions greater than five. The interesting ramification of thisresult is a new interpretation of the structure of the regular free boundary close to singular points. Forfurther details and references see: https://www.scilag.net/problem/P-200218.1.
Nonlocal models for traffic flowWen Shen
The Pennsylvania State University, USA
In this talk we consider nonlocal models for traffic flow, where the drivers take into considerationof the information in front of them. A brief overview of recent results will be given. In particular,we proved the nonlocal to local limit. Here, the uniform bound on the total variation is achieved byrewriting the equation into a relaxation system, and the entropy condition is established thanks to theHardy-Littlewood inequality.
Euler equations, transonic flows and isometric embeddingsDehua Wang
University of Pittsburgh, USA
In this talk, we will discuss the Euler equations of gas dynamics and applications in transonic flowsand isometric embeddings in geometry. First the basic theory of Euler equations will be reviewed.Then we will present the results on the transonic flows past an obstacle including the global existenceof weak solutions. Finally we will present the fluid dynamic formulation of the isometric embeddingproblems in geometry and discuss the global solutions based on various approaches.
12
Threshold Dynamics Method and ApplicationsXiao-Ping Wang
Hong Kong University of Science and Technology, Hong Kong, China
The threshold dynamics method is an efficient method for simulating the motion by mean curvatureflow. The method alternately diffuses and sharpens characteristic functions of regions and is easy toimplement and highly efficient. It can also be applied to more general interface problems. I will givean introduction of the threshold dynamics method and its generalizations, analyzing their properties.Applications to the interface motion in multiphase flow, image processing and topology optimizationwill also be presented.
Phase transition solutions to a hyperbolic-parabolic system modelingvascular networks
Zhi-an Wang
The Hong Kong Polytechnic University, Hong Kong, China
Blood vessel network formation in vitro demonstrates that endothelial cells randomly dispersingon a gel substrate (matrix) can spontaneously organize into connected capillary networks with phasetransitions. This phenomenon has been called in vitro angiogenesis - a major factor of tumor growth.How endothelial cells self-organize geometrically into capillary networks and how individual cells coop-erate to form the coherent patterns remain poorly understand biologically up to date. These coherentnetwork patterns cannot be explained by the macroscopic chemotaxis models that lead to point-wiseblowup or rounded aggregates, nor by the microscopic chemotaxis models that describe single cell be-haviors. However the damped hydrodynamic (hyperbolic-parabolic) chemotaxis model can numericallyreproduce the key features of remarkable networking patterns. In this talk, we shall report a resulton the stability of phase transition steady states to this hyperbolic-parabolic system in the half spacewith Dirichlet boundary conditions under some structure assumptions on the pressure function.
Global well-posedness and time-decay estimates for compressibleNavier-Stokes equations with reaction diffusion
Huanyao Wen
South China University of Technology, China
We consider the compressible Navier-Stokes equations with reaction diffusion. Some optimal time-decay estimates of the solution are derived when the initial perturbation is additionally bounded in L1.In particular, there is no decay loss for the highest-order spatial derivatives of the solution. The aboveresult is also valid for compressible Navier-Stokes equations. The proof is accomplished by virtue ofFourier theory and an observation for cancellation of a low-frequency quantity. This talk is based ona joint work with Prof. Wenjun Wang.
13
Hyperbolic boundary problems with large oscillatory lower orderterms: multiple amplification
Mark Williams
University of North Carolina-Chapel Hill, USA
We consider the well-posedness of linear hyperbolic boundary problems with large oscillatory lowerorder terms. We are especially interested in problems where waves with special frequencies are “multi-ply amplified” as they reflect off the boundary. Such problems arise in the study of stability of shocksand vortex sheets.
Convexity and uniqueness of the regular shock reflection for thepotential flow
Wei Xiang
City University of Hong Kong, Hong Kong, China
We will talk about our recent results on the uniqueness of regular reflection solutions for thepotential flow equation in a natural class of self-similar solutions. The approach is based on a nonlinearversion of the method of continuity. An important property of solutions for the proof of uniqueness isthe convexity of the free boundary.
Analysis on steady compressible jet flows with nonzero vorticityChunjing Xie
Shanghai Jiao Tong University, China
In this talk, we discuss the recent progress on subsonic steady jet flows with nonzero vorticity.One of the key ingredients for the analysis is exploration of the variational structure of quasilinearlinear equations for the stream function even when there is nonzero vorticity. Then the frame work byAlt, Caffarelli, and Friedman for free boundary problem together with some techniques such as uniquecontinuation for elliptic equations gives the existence and uniqueness of the solutions.
14
Conducting fluids with a moving physical boundaryFeng Xie
Shanghai Jiao Tong University, China
In this talk, we will discuss the validity of Prandtl boundary layer expansion for the solutions totwo dimensional steady viscous incompressible MHD equations under high Reynolds numbers assump-tions in a domain (X,Y ) ∈ [0, L] × R+ (L suitably small) with a moving flat boundary Y = 0.As a direct consequence, the inviscid limit is thus established for the solution of 2D steady viscousincompressible MHD equations in Sobolev spaces provided that the following three assumptions hold:the hydrodynamics and magnetic Reynolds numbers take the same order in term of the reciprocal of asmall parameter ϵ, the tangential component of the magnetic field does not degenerate near the bound-ary and the ratio of the strength of tangential component of magnetic field and tangential componentof velocity is suitably small. This talk is based on the joint work with Prof. Shijin Ding, and Dr.Zhilin Lin.
On subsonic flows around a profile with a vortex lineZhouping Xin
The Chinese University of Hong Kong, Hong Kong, China
In this talk, I will present a result on the existence of 2-dimensional subsonic steady compressibleflows around a finite thin profile with a vortex line at the trailing edge, which is a special case inthe celebrated lifting line theory by Prandtl. Such a flow pattern is governed the two-dimensionalsteady compressible Euler equations. The vortex line attached to the trailing edge is a free interfacecorresponding to a contact discontinuity. Such a flow pattern is obtained as a consequence of structuralstability of a uniform contact discontinuity. Some ideas of the analysis will be presented. This talk isbased on joint works with Jun Chen and Aibin Zang at Yichun University. The research is supported inpart by Hong Kong Earmarked Research Grants CUHK 14305315, CUHK 14302819, CUHK 14300917,and CUHK 14302917.
The dissipative structure of compressible Navier-Stokes-Kortewegequations and its applications
Jiang Xu
Nanjing University of Aeronautics and Astronautics, China
We are concerned with a system of equations governing the evolution of isothermal, viscous andcapillary compressible fluids, which can be used as a phase transition model. It is observed by thepointwise estimate that the linear third-order Korteweg tensor behaves like the heat diffusion of den-sity fluctuation, which enables us to establish the global Gevrey analyticity and optimal time-decayestimates of Lq-Lr type. In addition, the general theory on the dissipative structure of symmetrichyperbolic-parabolic systems with Korteweg-type dispersion, is also developed.
15
Global existence and decay of solutions to Prandtl system with smallanalytic and Gevrey data
Ping Zhang
Chinese Academy of Sciences, China
In this talk, we shall prove the global existence and the large time decay estimate of solutions toPrandtl system with small initial data, which is analytical in the tangential variable. The key ingredientused in the proof is to derive sufficiently fast decay-in-time estimate of some weighted analytic energyestimate to a quantity, which consists of a linear combination of the tangential velocity with its primitiveone, and which basically controls the evolution of the analytical radius to the solutions.Our result canbe viewed as a global-in-time Cauchy-Kowalevsakya result for Prandtl system with small analyticaldata,which in particular improves the previous result in [IV16] concerning the almost global well-posedness of two-dimensional Prandtl system. In the last part, I shall also mention our recent resulton the global well-posedness of this system with optimal Gevrey data. (This is partially joint workwith Ning Liu, Marius Paicu, Chao Wang and Yuxi Wang).
Some recent studies on steady MHD boundary layersZhu Zhang
City University of Hong Kong, Hong Kong, China
In this talk, I will present a recent result on the two dimensional steady MHD boundary layers. Weprove the nonlinear stability of shear flows of Prandtl type with nondegenerate tangential magneticfield, but without any positivity or monotonicity assumption on velocity field. Unlike the unsteadyMHD system, we manage the degeneracy on the boundary caused by non-slip boundary conditionand obtain the estimates of solutions by introducing an intrinsic weight function and some auxiliaryfunctions. This is a joint work with Prof. Cheng-jie Liu and Prof. Tong Yang.
Global regularity for Einstein-Klein-Gordon system with U(1)× Risometry group
Yi Zhou
Fudan University, China
We prove the global regularity of the 3+1 dimensional Einstein-Klein-Gordon system with a U(1)×R isometry group. We reduce the Cauchy problem of the Einstein-Klein-Gordon system to a 2+1dimensional system. We prove that the energy of this system cannot concentrate near the first possiblesingularity, and hence is small. Then, we show that the global regularity holds for the reduced 2+1dimensional system with initial data of small energy.
16
New phase-field models for martensitic phase transformations withapplications to MGI
Peicheng Zhu
Shanghai University, China
We shall talk about some new phase-field models for martensitic phase transformations driven bymaterial forces, occurring smart materials such as Shape memory alloys. These models are elliptic-parabolic coupled systems which differ, by a non-smooth gradient term, from the well-known modelsof the Allen-Cahn type. The models can also be applied to Materials Genome Initiative that waslaunched by former American president Obama in 2011 to accelerate the innovation of new materials.
17
a
Abstracts(Youth Forum)
18
Local strong solutions to the full compressible Navier-Stokes systemwith temperature-dependent viscosity and heat conductivity
Yue Cao
Shanghai Jiao Tong University, China
In this talk, we study the full compressible Navier-Stokes equations in a bounded domain Ω ⊂R3, where the viscosity and heat conductivity depend on the temperature θ in a power law (θb) ofChapman-Enskog. We proved the local existence of strong solution to the initial-boundary valueproblem with initial vacuum and arbitrarily large data. This local existence is not trivial especially forthe non-isentropic system with vacuum, and temperature-dependent viscosity and heat conductivity.There are extremely strong nonlinearity in the system, which brings great difficulty in the a prioriestimates, especially the second-order estimates of the solution. In order to overcome these difficulties,we found a new method to provide better estimates to the second-order derivatives of the velocity andtemperature, which plays a key role in closing the a priori estimates. We also introduce a new variableto reformulate the system into a better form and require the measure of the initial vacuum domainis sufficiently small, for example, the initial vacuum only appears in some one-dimensional curves ortwo-dimensional surfaces. Moreover, the result holds for the case that µ, λ ∼ θb1 and κ ∼ θb2 withconstants b2 + 1 > b1 ≥ 0.
Blow-up of solutions to Nakao’s problem via an iteration argumentWenhui Chen
Shanghai Jiao Tong University, China
In this paper, we consider blow-up behavior of weak solutions to a weakly coupled system for asemilinear damped wave equation and a semilinear wave equation in the whole space. This problem ispart of the so-called Nakao’s problem proposed by Professor Mitsuhiro Nakao (Kyushu university) fora critical relation between the exponents p and q of the power nonlinearities. By applying an iterationmethod for unbounded multipliers with a slicing procedure, we prove blow-up of weak solutions forNakao’s problem even for small data. We improve the blow-up result and upper bound estimates forlifespan comparing with the previous research, especially, in higher dimensional cases. This work isjoint with Professor Michael Reissig (TU Freiberg).
Global strong solutions to the two-dimensional full compressibleNavier-Stokes equations with large viscosity
Hao Li
Shanghai Jiao Tong University, China
In this talk, we consider the initial-boundary value problem for the full compressible Navier-Stokesequations on the square domain. We show that the strong solution exists globally in time if thecoefficient of viscosity is suitably large. Moreover, the exponential decay rate of the strong solutionis obtained.
19
Boundary Hölder regularity for fully nonlinear elliptic equations onReifenberg flat domains
Yuanyuan Lian
Shanghai Jiao Tong University, China
In this note, we investigate the boundary Hölder regularity for fully nonlinear elliptic equations onReifenberg flat domains. We will prove that for any 0 < α < 1, there exists δ > 0 such that the solutionsare Cα at x0 ∈ ∂Ω provided that Ω is (δ,R)-Reifenberg flat at x0. A similar result for the Poissonequation has been proved by Lemenant and Sire, where the Alt-Caffarelli-Friedman’s monotonicityformula is used. Besides the generalization to fully nonlinear elliptic equations, our method is simple.In addition, even for the Poisson equation, our result is stronger than that of Lemenant and Sire.
On Dirichlet problem for the fractional LaplacianChenkai Liu
Shanghai Jiao Tong University, China
In our research, we study the existence and uniqueness of Dirichlet problem for fractional Lapla-cian. First, we introduce a weighted integrability condition that precisely describes the existence anduniqueness condition for Dirichlet problem of fractional Laplacian on the unit ball. Then we applyPerron’s method to derive the existence of Green’s function on more general domains. Based on this,we derive a similar well-posedness condition for fractional Laplacian on more general domains.
Low mach number limit and far field convergence rates of potentialflows in multi-dimensional nozzles with an obstacle inside
Lei Ma
Shanghai Jiao Tong University, China
This paper considers the low Mach number limit and far field convergence rates of steady Eulerflows with external forces in three-dimensional infinitely long nozzles with an obstacle inside. First,the well-posedness theory for both incompressible and compressible subsonic flows with external forcesin multidimensional nozzle with an obstacle inside are established by several uniform estimates. Theuniformly subsonic compressible flows tend to the incompressible flows as quadratic order of Machnumber as the compressibility parameter goes to zero. Furthermore, we also give the convergence ratesof both incompressible flow and compressible flow at far fields as the boundary of nozzle goes to flateven when the forces do not admit convergence rate at far fields. The convergence rates obtained forthe flows at far fields clearly describe the effects of the external force.
20
Incompressible Navier-Stokes-Fourier limit from the Landau equationMohamad Rachid
Université de Nantes, France
In this talk, we are interested in the Landau equation which is a kinetic model in plasma physicsthat describes the evolution of the density function f = (t, x, v) representing at time t ∈ R+ thedensity of particles at position x ∈ T3 (the 3-dimensional unit periodic box) and velocity v ∈ R3. Westudy the Landau equation, depending on the Knudsen Number and its limit to the incompressibleNavier-Stokes-Fourier equation on the torus. We prove uniform estimate of some adapted Sobolevnorm and get existence and uniqueness of solution for small data. These estimates are uniform inthe Knudsen number and allow to derive the incompressible Navier-Stokes-Fourier equation when theKnudsen number tends to 0.
Global existence of classical solutions to the two-dimensionalcompressible Boussinesq equations in a square domain
Zhaoyang Shang
Shanghai Jiao Tong University, China
In this talk, we consider the initial boundary value problem of two-dimensional isentropic compress-ible Boussinesq equations with constant viscosity and thermal diffusivity in a square domain. Based onthe time-independent lower-order and time-dependent higher-order a priori estimates, we prove thatthe classical solution exists globally in time provided the initial mass of the fluid is small. Here, wehave no small requirements for the initial velocity and temperature.
Suppression of blow up by mixing in generalized Keller-Segel systemwith fractional dissipation
Binbin Shi
Shanghai Jiao Tong University, China
In this paper, we consider the Cauchy problem for a generalized parabolic-elliptic KellerSegelequation with a fractional dissipation and an additional mixing effect of advection by an incompressibleflow. Under a suitable mixing condition on the advection, we study well-posedness of solution withlarge initial data. We establish the global L∞ estimate of the solution through nonlinear maximumprinciple, and obtain the global existence of classical solution.
21
On the interaction between compressible viscous fluids and platesSrđan Trifunović
University of Novi Sad, Serbia
Here, I will talk about a nonlinear interaction problem between compressible viscous fluids andplates. Two recent results will be presented:
• S.T., Y.-G. Wang, On the interaction problem between a compressible viscous fluid and a non-linear thermoelastic plate, arxiv: 2010.01639;
This result concerns the existence of a weak solution to such a problem, which was obtainedby constructing a time-continuous approximation scheme which decouples the fluid and the plate.
• S.T., Y.-G. Wang, Compressible viscous fluids interacting with plates - suitable weak solutionsand weak-strong uniqueness, preprint.
In this result, a class of suitable weak solutions for this problem is introduced - a sub-classof bounded energy weak solutions. First, it is proved that these solutions have the weak-stronguniqueness property, then this class is characterized. In particular, if adiabatic constant γ > 3in 3D (or γ > 1 in 2D), then suitable weak solutions ≡ bounded energy weak solutions.
Partial exact boundary synchronization and partial approximateboundary synchronization for a coupled system of wave equations
Chenmu Wang
Shanghai Jiao Tong University, China
The lecturer proposes the concept of partial exact boundary synchronization and partial ap-proximate boundary synchronization for a coupled system of wave equations with Dirichlet bound-ary controls, and makes a deep discussion on them. We obtain necessary and sufficient conditionsfor the realization of partial exact boundary synchronization. And sufficient conditions to realize thepartial approximate boundary synchronization and necessary conditions of Kalman’s criterion. Meanwhile,the lecturer studies the partial synchronizable state and obtain a sufficient condition to guarantee thatthe partial synchronizable state does not depend on applied boundary controls. In addition, with thehelp of partial synchronization decomposition, a sufficient condition that the approximately synchro-nizable state does not depend on the sequence of boundary controls is also given.
22
Classification of positive solutions for fully nonlinear elliptic equationsin unbounded cylinder
Lidan Wang
Shanghai Jiao Tong University, China
In this paper, we consider the positive viscosity solutions for certain fully nonlinear uniformly ellipticequations in unbounded cylinder with zero boundary condition. After establishing an Aleksandrov-Bakelman-Pucci maximum principle, we classify all positive solutions as three categories in unboundedcylinder. Two special solution spaces (exponential growth at one end and exponential decay at the an-other) are one dimensional, independently, while solutions in the third solution space can be controlledby the solutions in the other two special solution spaces under some conditions, respectively.
The closed range property for the d-bar operatorQianyun Wang
Shanghai Jiao Tong University, China
In this talk, we will introduce the closed range property for the d-bar operator. We study the closedrange property for the d-bar operator on the unit disc, the punctured disc, and the annulus endowedwith their Poincare metrics, respectively. The necessary conditions for the closed range property of thed-bar operator are also given on these domains with the Kahler metrics. On a special Stein domain,we also consider the closed range property.
On the construction of blowing-up solutions to some nonlinear ellipticequations
Shaodong Wang
Shanghai Jiao Tong University, China
In this talk, I will present some recent work on the construction of blowing-up solutions to someYamabe-type PDEs on manifolds with boundary. We will use the method of bubble accumulation andfinite dimensional reduction to obtain infinitely many solutions with unbounded energy.
23
On the back flow of the mixed Prandtl-Hartmann boundary layerproblemXiang Wang
Shanghai Jiao Tong University, China
The proposal of this paper is to study the effect of magnetic field in stabilizing the hydrodynamicflow and preventing the occurrence of back flow in the Prandtl-Hartmann boundary layer. Under themonotonicity condition, we obtain that a first back-flow point, when the boundary layer evolves intime, should appear on the boundary if it occurs, notably the pressure gradient of the outer flow isnot necessarily adverse. Moreover, when the adverse pressure gradient of the outer flow dominatesthe orthogonal magnetic field, and the initial velocity satisfies certain growth condition, we obtain theexistence of a back-flow point of the Prandtl-Hartmann boundary layer.
Global existence and large time behavior for the chemotaxis–shallowwater system in a bounded domain
Yucheng Wang
Shanghai Jiao Tong University, China
In this paper, we consider the chemotaxis–shallow water system in a bounded domain Ω ⊂ R2.By energy method, we establish the global existence of strong solution with small initial perturbationand obtain the exponential decaying rate of the solution. We divide the bounded domain into interiordomain and the domain up to the boundary. In the interior domain, the problem is treated like theCauchy problem. In the domain up to the boundary, the tangential and normal directions are treateddifferently. We use different method to get the estimates for the tangential and normal directions.
Mild solutions of the stochastic MHD equations driven by fractionalBrownian motions
Zirong Zeng
Shanghai Jiao Tong University, China
In this talk, the incompressible magnetohydrodynamic equations driven by additive fractional Brow-nian motions are considered. The local existence and uniqueness of the mild solution in Lp space on asmooth bounded domain in Rd (d = 2, 3) are firstly studied. The proof is based on the semigroup the-ory, fixed point theorem and the results of stochastic PDEs of linear parabolic type. In the proof, theeigenvalue problem with perfectly conducting wall condition is considered to weaker the requirementsof noise terms. The global existence of mild solutions is also established by energy estimate.
24
The rigorous derivation of unipolar Euler-Maxwell system forelectrons from bipolar Euler-Maxwell system by infinity-ion-mass limit
Liang Zhao
Shanghai Jiao Tong University, China
In this talk, we consider the local-in-time and the global-in-time convergence of infinity-ion-masslimit for bipolar Euler-Maxwell systems by setting the mass of an electron me = 1 and letting themass of an ion mi → +∞. We use the method of asymptotic expansions to handle the local-in-time convergence problem and find that the limiting process from bipolar models to unipolar modelsis actually decoupling, but not the vanishing of equations for the corresponding the other particle.Moreover, when the initial data is sufficiently close to the constant equilibrium state, we also establishthe corresponding global-in-time convergence.
On the compactness of conformally compact Einstein manifoldHuihuang Zhou
Shanghai Jiao Tong University, China
Given a sequence of conformally compact Einstein manifold with a compact family of metrics onboundary, we are interested in the compactness issue. Recently Chang-Ge-Qing proved some compact-ness results of conformally compact Einstein metric on 4-dimensional manifold with Fefferman-Grahamcompactification. In this talk, we consider the compactness with other two special compactification,Lee compactification and the adapted compactification. We prove the equivalence of compactnessbetween the three special compactification.
25