【学术报告】Global solutions to the incompressible ideal MHD (I)(II)

报告人：蔡圆（复旦大学）

时 间：2024年11月20日15:00 & 2024年11月21日15:00

地 点：厦门大学海韵园实验楼S105&S107

内容摘要:

This series talks consist of two parts. In the first part, we study the Cauchy problem of the incompressible ideal (inviscid and non-resistive) magnetohydrodynamics. Under the assumption that the initial velocity field and the displacement of the initial magnetic field from a non-zero constant state are sufficiently small in certain weighted Sobolev spaces, we show the global in time existence of solutions.

In the second part, we study the global current-vortex sheets in the two-dimensional ideal incompressible MHD. The magnetohydrodynamic current-vortex sheet is a free boundary problem involving a moving free surface separating two plasma regions. We prove the global nonlinear stability of current-vortex sheet in the two dimensional ideal incompressible magnetohydrodynamics under the strong horizontal background magnetic field. This appears to be the first result on the global solutions of the free boundary problems for the ideal (inviscid and non-resistive) incompressible rotational fluids. These are based on the joint works with Professor Zhen Lei.

个人简介：

蔡圆，复旦大学数学科学学院青年副研究员。研究方向为流体力学中的偏微分方程，在流体力学方程组解的整体粘性消失等方面作出了多项重要研究成果，部分论文发表在CPAM、JMPA、ARMA、JFA、SIMA等国际著名刊物。2019年获第二届全国偏微分方程博士生论坛优秀论文奖，2020年获香港研究资助局一般面上项目资助，2022年入选上海市领军人才（海外）青年人才项目。

联系人：王焰金