报告题目：Optimal Large Time Behavior for the 3D Compressible MHD System with Discontinuous Initial Data

主 讲 人：张 映 辉

单 位：广西师范大学

时 间：10月10日15:00

地 点：数学院一楼报告厅

摘 要：

This talk is concerned with large time behavior of the weak solutions to the 3D compressible MHD system with discontinuous initial data. The global existence of weak solutions to the Cauchy problem of the 3D compressible MHD system has been established by Suen-Hoff [36] (also see [30]), under the condition that the initial energy is suitably small, the initial density is positive and essentially bounded and the gradients of initial velocity and magnetic field are bounded in L^2. However, to our best knowledge, so far there is no result on time-decay rates of such solutions. The main novelty of this paper is to give a positive response to this problem. More precisely, we obtain the optimal time-decay rates of the solutions in L^r-norm with 2 ≤ r ≤ ∞and the first order derivatives of the velocity and magnetic field in L^2-norm when the L^1-norm of the initial perturbation is bounded. Moreover, we also show the lower bounds on the rates of decay.

简 介：

张映辉，教授，博士生导师，现任广西师范大学数学与统计学院副院长。广西杰出青年基金获得者，广西高等学校中青年骨干教师，广西师范大学A类漓江学者，美国佐治亚理工学院和加拿大不列颠哥伦比亚大学访问学者，美国《数学评论》评论员，国际期刊《SCIREA Journal of Mathematics》编委。主要研究方向为偏微分方程理论及其应用。主持国家自然科学基金2项，国家自然科学基金子项目2项，广西杰出青年科学基金、博士后基金等省部级项目20余项；以独立作者、第一作者或通讯作者身份在SIAM J. Math. Anal.、J. London Math. Soc.、Indiana U. Math. J.、J. Differ. Equations、P. Roy. Soc. Edinb A、Sci. China Math.等国际著名期刊上发表SCI论文40余篇；出版英文学术专著1部；获省自然科学奖和市科技进步奖各1项。