关于举行上海交通大学李亚纯教授学术报告会的通知

报告题目：Vanishing Viscosity Limit of the Navier-Stokes Equations to the Euler Equations for Compressible Fluid Flow with degenerate viscosities and vacuum

报  告  人：李亚纯  教授(上海交通大学)

报告时间：2019年9月19日（星期四）14:30-15:10                

报告地点：4号楼4318室

邀  请  人：朱长江教授，温焕尧教授

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数学学院

2019年9月17日

报告摘要：

We establish the vanishing viscosity limit of the Navier-Stokes equations to the Cauchy problem of Euler equations for three- dimensional compressible isentropic flow. When the viscosity coefficients are given as constant multiples of the density's power，we prove 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.

报告人简介： 

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，先后主持了国家自然科学基金项目十余项，入选了上海市曙光人才计划、教育部新世纪优秀人才计划等，与同事合作获得上海市自然科学一等奖。