报告题目：Global small solutions of heat conductive compressible Navier-Stokes equations with vacuum: smallness on Scaling invariant quantity
报 告 人： 李进开 教授
工作单位：华南师范大学
报告时间：2020-10-28(周三) 15:00-16:00
腾讯会议ID：516 671 915
报告摘要：
In this talk, I will present the global well-posednessof strong solutions to the Cauchy problem of the heat conductive compressible Navier-Stokes equations in the presence of initial vacuum. Global existence is established under the assumption, among some other necessary regularity and compatibility conditions, that a certain scaling invariant quantity is sufficiently small, with the smallness depending only on the parameters involved in the system. Notably, the smallness assumption is imposed exclusively on the scaling invariant quantity mentioned above, and it is independent of any norms of the initial data; this is different substantially from the related existing works. The total mass can be either finite or infinite. An equation for the density, more precisely for the cubic of the density, derived from combing the continuity and momentum equations, will be employed to get the a priori L1(L3) estimate of the density.
报告人简介：
华南师范大学华南数学应用与交叉研究中心教授，博士生导师，2018年入选国家海外高层次人才引进计划青年项目。2013年博士毕业于香港中文大学数学科学研究所，导师为辛周平教授。2013至2016于以色列威兹曼科学研究所(Weizmann Institute of Sciences)从事博士后研究工作，合作导师为EdrissS. Titi教授。2016至2018在香港中文大学数学系任研究助理教授。2018年其至今在华南师范大学华南数学应用与交叉研究中心工作。主要从事流体动力学方程方面的研究，主要包括大气海洋动力学偏微分方程(以Primitive Equatgions为代表)、Navier-Stokes方程组、复杂流体等。目前已在包括CPAM, Adv. Math, JFA, ARMA, CPDE, SIMA等国际学术期刊上发表SCI论文30篇，主持国家自然科学基金面上项目1项，香港研究资助局面上项目1项，广东省自然科学基金面上项目1项，粤港澳应用数学中心项目1项。
