时间：2023年4月7日（本周五）下午2:30-4:30
地点：理科楼A404
组织者：于品
报告一
标题：Analysis of steady flows with stagnation points for the incompressible Euler system in an infinitely long nozzle
报告人：谢春景（教授，上海交通大学）
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。
报告二
标题：Hidden structures behinds the compressible Navier-Stokes equations and its applications to the corresponding models
报告人：黄祥娣（研究员，中国科学院数学与系统科学研究院）
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.
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奖，并在2022年第九届世界华人数学家大会做一小时报告，同年主持了第二批中科院稳定支持基础研究青年团队计划。
