报 告 人： 蔡圆 复旦大学
题 目： Global solutions to the incompressible MHD near equilibrium
报告时间：2024年8月10日(星期六) 9:00-11:00
报告地点：数信学院 305
摘要：This talk concern two problems in incompressible magnetohydrodynamics (MHD). One is the Cauchy problem of the MHD system with or without viscosity. Under the assumption that the initial velocity field and the displacement of the initial magnetic field from a non-zero constant are sufficiently small in certain weighted Sobolev spaces, the Cauchy problem is shown to be globally well-posed for all time and all space dimension n>1. The second one concerns the Cauchy problem of the incompressible non-resistive MHD in the whole three-dimensional space near equilibrium. The global solution has been obtained by Li Xu, Ping Zhang (under some admissible condition) and by Hammadi Abidi, Ping Zhang (removing the admissible condition) in anisotropic Besov space framework. We report our new temporal weighted energy method proof on this problem. These works are in part joint with Professor Zhen Lei, Bin Han and Na Zhao.
个人简介：蔡圆，复旦大学数学科学学院青年研究员。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。
