科研进展与学术交流报告会

（第14期）

报告人一： 黄祥娣 研究员（数学研究所）    

题 目 一：Hidden structures behinds the compressible Navier-Stokes equations and its applications to the corresponding models  

摘 要 一：In this talk, we will review the past developments on the solutions of the compressible Navier-Stokes equations and reveal the three hidden structures which linked the weak solution to the strong one.   Based on these observations, we proved the Nash's conjecture in 1958s and establish global exsitence theory for both isentropic and heat-conductive compressible Navier-Stokes equations.       

Moreover, for the 3D compressible Navier-Stokes equations, we will show the existence of local weak solutions with higher regularity and local strong solutions with lower regularity. Also, we will mention the recent results on the blowup of the local strong solutions to the MHD equations in finite time and global existence of weak solutions of the compressible Navier-Stokes equations in bounded domains under Dirichlet boundary conditions.  

报告人二： 王益 研究员（应用数学研究所）    

题 目 二：可压缩Navier-Stokes方程Riemann解的稳定性    

摘 要 二: 可压缩Navier-Stokes方程描述可压缩粘性流体运动的力学规律，是流体力学中的基本方程。如果忽略粘性效应，可压缩Navier-Stokes方程即为无粘的可压缩Euler方程。可压缩Euler方程描述理想流体的运动，是典型的双曲守恒律方程组，其主要特点是：无论初值多么光滑和多么小，解都可能会爆破，形成间断（激波）。如果考虑可压缩Euler方程的Riemann问题，其解具有三种基本波：激波、稀疏波和接触间断波，这三种基本波及其组合统称为Riemann解。Riemann解不仅决定了可压缩Euler方程解的局部和整体性质，而且决定了可压缩Navier-Stokes方程解的渐近行为。本报告将报告可压缩Navier-Stokes方程Riemann解的渐近稳定性的相关结果，特别是我们在等熵可压缩Navier-Stokes方程Riemann解的稳定性方面取得的最新研究进展。    

时  间：2022.11.25(星期五), 10:40-13:00    

地  点：腾讯会议991-7305-6661    

报告会视频