江苏省应用数学（集团）中心系列学术报告

Title：Singularity formation for fluid models

Speaker：Professor Mimi Dai（戴觅秘）

Time：October 20, 2023（Friday）10:00-11:00 (Beijing Time)

Address：Online

VOOV Number (Tencent)：5318371238

Link:https://meeting.tencent.com/p/5318371238

Abstract：Finite time singularity formation for fluid equations will be discussed. Built on extensive study of approximating models, breakthroughs on this topic have emerged recently for Euler equation. Inspired by the progress for pure fluids, we attempt to understand this challenging issue for magnetohydrodynamics (MHD). Finite time singularity scenarios are discovered for some reduced models of MHD. The investigation also reveals connections of MHD with Euler equation and surface quasi-geostrophic equation.

Introduction：

Mimi Dai, Professor in Mathematics at the University of Illinois at Chicago (UIC). Dai obtained her PhD in mathematics from the University of California at Chicago. She was a postdoctoral researcher at the University of Colorado at Boulder and UIC. After spending a year at the Institute for Advanced Study, Princeton as a von Neumann Fellow, and at Princeton University as a visiting professor, she is now a full professor at UIC.

 Dai's research within the rather broad area of partial differential equations (PDEs) has been centered around open problems in turbulent flows, governed by the incompressible Navier-Stokes equation (NSE), such as the issues of unique solvability and the appearance of singularity, through the lenses of functional analysis, harmonic analysis, convex integration, etc. Some of the methods are motivated by ideas from physics and other disciplines of mathematics. In addition to the NSE hydrodynamics, Dai's interest has also been extended to other PDEs, for instance, magnetohydrodynamics (MHD) which is of fundamental importance in plasma physics and the surface quasi-geostrophic (SQG) equation describing geophysical flows in atmosphere and oceanography.