补偿列紧理论及其在双曲型偏微分方程中的应用
[TMCSC]
9月14日 14:30--17:00 p.m.
9月15/16/17日 09:00--11:30 a.m.
地点:四川大学望江校区国家天元数学西南中心516报告厅
![[minicourse ]王勇-01.png](http://tianyuan.scu.edu.cn/upload/default/20210907/%5Bminicourse%20%5D%E7%8E%8B%E5%8B%87-01.png "[minicourse ]王勇-01.png")
SPEAKER
王勇（中国科学院数学与系统科学研究院）
ABSTRACT
本课程主要讲解补偿列紧的基本理论及其在双曲型偏微分方程大初值整体弱解存在性中的应用，具体内容如下：
1）双曲型偏微分方程的基本概念和重要模型；
2）弱收敛基本理论；
3）Young Measure 定理 及 Div-Curl 引理；
4）补偿列紧理论的应用
SUPPORTED BY
国家天元数学西南中心
四川大学数学学院
学术研讨会安排
时间地点：祥宇宾馆
2021年9月17日下午：
15：00-15：50
报告人 曹文涛
题目 Isometric immersions and compensated compactness
摘要： In this talk, the isometric immersion of two-dimensional Riemannian manifold with negative Gauss curvature into the three-dimensional Euclidean space is considered through the hyperbolic Gauss-Codazzi equations for the first and second fundamental forms. The large L∞ solution is obtained through compensated compactness approach, which leads to a C1,1 isometric immersion. The approximate solutions are constructed by adding artificial viscosity and the Lax-Friedrichs finite-difference scheme with the fractional step. The corresponding uniform estimates are achieved by maximum principle and studying some discrete ODEs respectively. This talk is based on joint results with Prof Feimin Huang and Prof Dehua Wang.
15:50-16:40
报告人：王勇
题目：Global Solutions of the Compressible Euler-Poisson Equations with Large Initial Data of Spherical Symmetry
摘要：We are concerned with a global existence theory for finite-energy solutions of the multidimensional Euler-Poisson equations for both compressible gaseous stars and plasmas with large initial data of spherical symmetry. One of the main challenges is the strengthening of waves as they move radially inward towards the origin, especially under the self-consistent gravitational field for gaseous stars. A fundamental unsolved problem is whether the density of the global solution forms concentration to become a delta measure at the origin. To solve this problem, we develop a new approach for the construction of approximate solutions as the solutions of an appropriately formulated free boundary problem for the compressible Navier-Stokes-Poisson equations with a carefully adapted class of degenerate density-dependent viscosity terms, so that a rigorous convergence proof of the approximate solutions to the corresponding global solution of the compressible Euler-Poisson equations with large initial data of spherical symmetry can be obtained. Even though the density may blow up near the origin at certain time, it is proved that no concentration (delta measure) is formed in the vanishing viscosity limit for the finite-energy solutions of the compressible Euler-Poisson equations for both gaseous stars and plasmas in the physical regimes under consideration.
16:40-17:10 茶歇
17:10-18:00
报告人：袁迪凡
题目：Stabilization Effect of Elasticity on compressible vortex sheets
摘要：In this talk, I will introduce vortex sheets phenomena in compressible inviscid flow in elastodynamics. Vortex sheets in compressible Euler flows are classical subjects in the study of hydrodynamics which date back to 1950's. This is a nonlinear hyperbolic problem with a characteristic free boundary. Three dimensonal elastic vortex sheets have complicate interactions between the effects of elasticity and the fluid velocity, making the mathematical analysis more challenging. In the end, I will introduce some recent results, which are closely related to the geometric properties of the elastic deformation gradient. This is a joint work with Prof Ming Chen, Prof. Feimin Huang and Prof. Dehua Wang.
18:00 晚餐
会议议程
