含真空的可压缩流体N-S方程到Euler方程的粘性消失极限

主讲人：李亚纯 上海交通大学数学科学学院教授 博士生导师

时间：2019年6月13日10：00

地点：徐汇校区3号楼332报告厅

举办单位：数理学院

主讲人介绍：李亚纯，上海交通大学数学科学学院教授，博士生导师。长期从事非线性偏微分方程的理论与应用研究，近年来在流体力学方程组的数学理论研究方面发表相关论文40余篇，并有多篇论文被收录在专著或系列丛书中，出版英文译著两本。先后主持了国家自然科学基金项目十余项（包括重点项目一项），上海市自然科学基金项目两项。入选上海市曙光人才计划、教育部新世纪优秀人才计划等项目，与同事合作获得上海市自然科学一等奖。  

内容介绍：We establish the vanishing viscosity limit of the Navier-Stokes equations to the  Euler equations for three-dimensional compressible isentropic flow in the whole  space. When the viscosity coefficients are given as constant multiples of the  density's power，it is shown that there exists a unique regular solution of  compressible Navier-Stokes equations with arbitrarily large initial data and  vacuum, whose life span is uniformly positive in the vanishing viscosity limit.  Via introducing a ``quasi-symmetric hyperbolic--``degenerate elliptic coupled  structure to control the behavior of the velocity of the fluid near the vacuum,  we establish some uniform estimates which lead the strong convergence of the  regular solution of the viscous flow to that of the inviscid flow, we also give  the rate of convergence. Furthermore, we point out that our framework is also  applicable to other physical dimensions, say 1 and 2, with some minor  modifications. This is a joint work with Yongcai Geng and Shengguo Zhu.