PDE系列报告
报告题目:Local weak and strong solution to the isentropic compreesible Navier-Stokes equations
报告人:黄祥娣 研究员
报告时间:2022年10月12日(周三)10:00-11:00
腾讯会议:255 481 290
报告摘要: In this talk, we present two recent works on the isentropic compressible NavierStokes equations. First, we prove the local existence and uniqueness of the strong solutions, where the initial compatibility condition proposed by Choe-Kim is removed under suitable sense.
Secondly, for periodic domain and half-space, we establish the existence of weak solutions with higher regularity of the threedimensional compressible isentropic Navier-Stokes equations in small time for the adiabatic exponent $\gamma>1$ in the presence of vacuum. It can be viewed as a local version of Hoff's work, and also extends the result of Desjardins by removing the assumption of $\gamma>3$.
报告人简介:黄祥娣,中国科学院数学与系统科学研究院研究员,主要研究高维可压缩Navier-Stokes方程。他的成果揭示了等熵和非等熵可压缩流体允许真空初值的光滑解在有限时刻爆破的机制,彻底解决并推广了诺贝尔奖得主J.Nash在1958年提出的关于可压缩流体光滑解爆破机制的猜想。在此基础上,他首次对等熵和非等熵流体建立了允许真空初值的整体光滑解和弱解,因此部分解决了菲尔兹奖得主P.L.Lions关于理想多方气体整体弱解存在性的猜想,其成果荣获2017年首届和2020年第四届世界华人数学家联盟年会的五年最佳论文银奖,并在2022年第九届世界华人数学家大会做一小时报告。