报告题目：Uniform regularity in the low Mach number and the inviscid limits for the non-isentropic Navier-Stokes system

摘要：

In fluid mechanics, an important physical quantity that measures the compressibility of a fluid is the so called Mach number. When it is very small, the compressible fluids tend to behave like the incompressible ones. This approximation process is referred to the low Mach numebr limit. We are interested in the justification of this limit process for the strong solutions to the compresible Navier-Stokes system in a domain with boundaries.

The crucial step towards this goal is to establish high regularity estimates uniformly in the Mach number, so that the solutions exist on a time interval independent of the Mach number.

In the first talk, we will focus on the propagation of the uniform regularity for the isentropic Navier-Stokes system in a domain either with fixed boundaries or with free boundaries. The appreance of the boundary layer with fast time oscillations are the main obstacle. These are joint works with Professors N. Masmoudi (NYU, Abu Dhabi) and F. Rousset (Orsay, France).

In the second talk, we study the more general non-isentopic viscous system and aim to prove the uniform estimates not only in the Mach number but also in the Reynolds number (another important physical quantity characterizing the viscosity of a fluid), which enables one to consider simultaneously the low mach number and the inviscid limits for strong solutions.

Compared to the isentropic system with estimates uniform only in the Mach number, some new difficulties arise due to the non-constant temperature and the interactions of two kinds of boundary layers.

报告人简介：孙长贞，现于法国图卢兹数学研究所从事博士后研究，研究方向为偏微分方程。2012-2016年就读于山东大学基地班，期间获潘承洞奖学金，国家奖学金。2016-2017年于中国科学院数学所进行硕士一年级学习，次年经张平老师推荐，赴法国巴黎萨克雷大学交流。之后获法国教育部奖学金并继续在该校攻读博士学位，2021年毕业于该校的奥赛实验室。

报告时间和地点：

2022年6月14日（周二）15:00-17:00， Zoom会议

2022年6月18日（周六）15:00-17:00， Zoom会议

邀请人：陶涛，山东大学数学学院副教授