短課題目：Convex Integration and Some Related Open Questions
授 課 人：BaishengYan Michigan State University
授課地點：2024年8月27日至9月10日, 數學樓 3樓教研室6(周二)，教研室1（周五）
預備知識：Partial differential equation, Real analysis and Convex analysis
課程簡介：
· 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
課程簡介：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).
