学 术 报 告

报告题目：Optimal decay rates of a non--conservative compressible two--phase fluid model

报告人：张映辉 教授  （广西师范大学）

报告时间：11月23 日下午3:00 – 4:00

报告地点：腾讯会议：318 567 841    

数学与统计学院

2020.11.17

报告摘要:We are concerned with the time decay rates of strong solutions to a non--conservative compressible viscous two--phase fluid model in the whole space $\mathbb R^3$. Compared to the previous related works, the main novelty of this paper lies in the fact that it provides a general framework that can be used to extract the optimal decay rates of the solution as well as its all--order spatial derivatives from one--order to the highest--order, which are the same as those of the heat equation. Furthermore, for well--chosen initial data, we also show the lower bounds on the decay rates. Our methods mainly consist of Hodge decomposition, low--frequency and high--frequency decomposition, delicate spectral analysis and energy method based on finite induction.

报告人简介:张映辉，博士，教授，博士生导师，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，现任广西师范大学数学与统计学院副院长。

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，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。