报告题目：Global solutions to the ideal incompressible MHD

报告人：蔡圆（复旦大学）

报告时间：2024年11月25日9:30-11:30

报告地点：数统学院A405

邀请单位：福州大学数学与统计学院

报告内容简介：

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 globally 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.

报告人简介：

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的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，SIAM 等国际著名刊物。曾获2019年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。