报告名称：Regularity criteria for weak solutions to the three-dimensional MHD system

主讲人：何娇 助理研究员

邀请人：冯泽夫 讲师

时间：2024年1月5日 15: 30

地点：十大网投正规信誉官网527会议室

主办单位：十大网投正规信誉官网

报告摘要

In this talk, I will first review various known regularity criterion and partial regularity theory for 3D incompressible Navier-Stokes equations.

I will then present two generalizations of the partial regularity theory of Caffarelli, Kohn and Nirenberg to the weak solutions of MHD equations. The first one is based on the framework of parabolic Morrey spaces. I will show parabolic Hölder regularity for the "suitable weak solutions" to the MHD system in small neighborhoods. This type of parabolic generalization using Morrey spaces appears to be crucial when studying the role of the pressure in the regularity theory and makes it possible to weaken the hypotheses on the pressure. The second one is a regularity result relying on the notion of "dissipative solutions". By making use of the first result, we will show the regularity of the dissipative solutions to the MHD system with a weaker hypothesis on the pressure. This is joint work with Diego Chamorro.

专家简介

何娇，巴黎萨克雷大学助理教授。2019年在法国里昂第一大学获得博士学位，2019-2021年在法国埃夫里大学从事博士后研究，之后在美国伯克利大学MSRI 继续博士后研究。2021年入职法国萨克雷大学。主要研究领域为偏微分方程，研究兴趣是解的正则性理论以及流体-固体中解的渐近行为。