勷勤数学•专家报告

题      目：Global current-vortex sheets in the two-dimensional ideal incompressible MHD

报  告  人：蔡圆  副研究员  (邀请人：李进开)

                                 复旦大学

时      间：12月17日  10：00-11：00

地     点：数科院西楼111报告厅

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 等国际著名杂志。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。

摘      要：

       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. The strong magnetic field plays a crucial role in the global in time stabilization effect. The proof relies on the understanding of the interplay between the dynamics of the fluids inside the domain and on the free interface, a design of multiple-level energy estimates with different weights, and the inherent structures of the problem. This is based on the joint work with Professor Zhen Lei.

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