Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars

Speaker:	陈嘉杰博士，Courant Institute, New York University
Inviter:
Title:	Singularity formation in incompressible fluids（Part I）
Language:	Chinese
Time & Venue:	2023.06.29 15:00-17:00 南楼N402
Abstract:	Whether the 3D incompressible Euler equations can develop a finite-time singularity from smooth initial data is an outstanding open problem. In the two parts of the lectures, I will discuss the recent development in singularity formation of 3D Euler equations with smooth initial data and boundary using a combination of analysis and rigorous numerics. Time permitting, I will discuss the following topics. (1) Major difficulties and existing methods. (2) Dynamic rescaling reformulation of the 3D Euler equations and construction of the approximate self-similar blowup profile. (3) Sharp Holder estimates, weighted energy estimates, and L^infty-based finite rank perturbation. (4) Some ideas and methods for rigorous numerics. These lectures are based on joint works with Tom Hou.