Title: Introduction to regularity of Navier Stokes equations and inviscid damping for Euler equations
Speaker: Professor Hao Jia (University of Minnesoda, USA)
Time: 10:00-11:30 on January 4 (Wen), January 6 (Fri), January 9 (Mon), January 11(Wen), January 13(Fri), January 16(Mon).
Zoom Link ID: 910 2659 9926
Abstract: In the first part of this series of lectures, we will introduce the regularity theory of Navier Stokes equations, starting with Leray's classical results on global weak solutions and local strong solutions. We will also present Kato's theory of mild solutions, and survey recent results on conditional global regularity results such as the celebrated Caffarelli-Kohn-Nirenberg partial regularity theory and Escauriaza-Seregin-Sverak $L^{3,\infty}$ regularity criteria, and potential singularity scenarios such as discretely self-similar solutions.
In the second part of the lectures, we will discuss some recent results in the inviscid damping problem for 2d Euler equations. These results include both linear and nonlinear inviscid damping results for monotonic shear flows and point vortices, and linear inviscid damping and vorticity depletion for general vortices and non-monotonic shear flows. The main emphasis will be on understanding the effect of continuous spectrum in the context of hydrodynamic stability problems.
主讲人简介：郏浩，美国明尼苏达大学副教授。2007年毕业于中国科学技术大学，2013年博士毕业于明尼苏达大学。2013年至2017年先后在芝加哥大学、普林斯顿高等研究院工作。主要研究兴趣是研究流体动力学方程和波动方程解的长时间动力学行为，特别在能量临界波动方程孤子预解猜想、Naiver-Stokes方程前向自相似解、管道内Couette流线性无粘阻尼、二维Euler方程点涡附近轴径向解、单调剪切流非线性无粘阻尼等领域研究取得一系列重要突破，部分研究成果发表在Acta Math., Invent. Math., CPAM, Geom. Funct. Anal., Amer. J. Math., CMP, ARMA等国际顶尖学术刊物。
