Sharp stability threshold for the 2D shear flows in the critical space
数学专题报告
报告题目(Title)：Sharp stability threshold for the 2D shear flows in the critical space
报告人(Speaker)：赵威任 助理教授 (New York University Abu Dhabi)
地点(Place)：Zoom ID：838 993 28728, 密码：123456, Zoom Link: https://us06web.zoom.us/j/83899328728
时间(Time)：2023 年 05 月 31 日(周三), 16:00-17:00
邀请人(Inviter)：薛留堂
报告摘要
In this talk, I will discuss a recent result about the asymptotic stability of a class of monotone shear flows for the two-dimensional incompressible free Navier-Stokes equation (without forcing) with small viscosity $\nu$. We obtain the sharp stability threshold $\nu^{1/2}$ for perturbations in the critical space $H^{log}_x L^2_y$. We also prove the enhanced dissipation and inviscid damping. In the proof, we construct a time-dependent wave operator corresponding to the Rayleigh operator, which could be useful in future studies. This is a joint work with Hui Li.
主讲人简介
赵威任博士，现为纽约大学阿布扎比(Abu Dhabi)分校的助理教授。主要方向是调和分析及其在流体力学方程中的应用，已在CPAM, ARMA, JMPA, Adv. Math., Mem. Amer. Math. Soc.等国际著名数学期刊发表多篇论文。
