English 清华大学 旧版入口 人才招聘




标题:Analysis of steady flows with stagnation points for the incompressible Euler system in an infinitely long nozzle
摘要Stagnation point in flows is an interesting phenomenon in fluid mechanics. It induces many challenging problems in analysis. We first derive a Liouville type theorem for Poiseuille flows in the class of incompressible steady inviscid flows in an infinitely long strip, where the flows can have stagnation points. With the aid of this Liouville type theorem, we show the uniqueness of solutions with positive horizontal velocity for steady Euler system in a general nozzle when the flows tend to the horizontal velocity of Poiseuille flows at the upstream. Finally, this kind of flows are proved to exist in a large class of nozzles and we also prove the optimal regularity of boundary for the set of stagnation points. This talk is based on joint work with Congming Li, Yingshu Lv, and Henrik Shahgholian.
报告人简介:谢春景,上海交通大学教授,2007年博士毕业于香港中文大学,在2011年加入上海交通大学之前,在香港中文大学和密西根大学做博士后。研究兴趣集中于高维流体力学方程组的适定性研究,特别是Euler方程组及其相关模型的亚音速解与跨音速解问题,定常Navier-Stokes方程组的适定性,以及高维Euler方程组弱解的不唯一性等。在Advances in Mathematics, Archive for Rational Mechanics and Analysis, Communications in Mathematical Physics等杂志发表多篇论文。

标题:Hidden structures behinds the compressible Navier-Stokes equations and its applications to the corresponding models
摘要: 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.