短课题目：Convex Integration and Some Related Open Questions
授 课 人：BaishengYan Michigan State University
授课地点：2024年8月27日至9月10日, 数学楼 3楼教研室6(周二)，教研室1（周五）
预备知识：Partial differential equation, Real analysis and Convex analysis
课程安排：
8月27日， 9：00-10：00； What is Convex Integration
8月27日， 14：00-15：00； Some process about Convex Integration
8月30日， 9：00-10：00；What type of PDE is suitable for Convex Integration
8月30日， 14：00-15：00； Some process about Convex Integration
9月3日， 9：00-10：00；How to apply convex integration to solve PDE
9月3日， 14：00-15：00 Irregular Solutions for elliptic Equations
9月6日， 9：00-10：00；Variational solutions of gradient flows
9月6日， 14：00-15：00； Irregular Solutions for Parabolic Equations
9月10日，9：00-10：00；Special polyconvex functionals and
9月10日，14：00-15：00； Some open questions about Convex Integration
课程简介：
· Convex integration is an important method originally developed to solve geometry and topology problems. This method has recently found remarkable applications in PDE, leading to many important results on the incompressible Euler equation and Navier-Stokes equation and to the resolution of some longstanding open problems.
· Part I: Introduction of Convex Integration
· Part II: Set up of PDE that is suitable for convex integration
· Part III: How to apply convex integration to solve PDE
· Part IV: Variational solutions of gradient flows for some convex integral functionals
· Part V: Special polyconvex functionals and some open questions
课程简介：Yan Baisheng is full-time professor at the Michigan state University. He got his PhD at University of Minnesota. He spent one year at Institute for Advanced Study. His main research interests are partial differential equations, calculus of variations, nonlinear elasticity and applications in continuum mechanics and materials science. Mainly, well-posedness (existence, uniqueness and stability of solutions).
