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

内容簡介：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.

報告人：蔡圓

報告人簡介：複旦大學數學科學學院青年副研究員。研究方向為流體力學中的偏微分方程，在流體力學方程組解的整體粘性消失的等方面作出了多項重要研究成果，部分論文發表在CPAM，JMPA，ARMA, JFA，SIAM 等國際著名刊物。曾獲2019年第二屆全國偏微分方程博士生論壇優秀論文獎，2020年獲香港研究資助局一般面上項目資助，2022年入選上海市領軍人才（海外）青年人才項目。

時  間：2024年12月20日（周五）10:30-11:30

地  點：石牌校區南海樓224室

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2024年12月12日