New energy method in the study of the instability near Couette flow
数学专题报告
报告题目(Title)：New energy method in the study of the instability near Couette flow
报告人(Speaker)：李徽 博士 纽约大学阿布扎比分校
地点(Place)：656-158-067
时间(Time)：2022年 6 月2 日 （周四）16:30-17:30
邀请人(Inviter)：袁迪凡
报告摘要
Hydrodynamic stability is an active field of fluid mechanics which deals with the stability and the instability of fluid flows. Mathematically, this kind of problems can be reduced to the study of the semi-group estimate related to the linearized operator. However, it is difficult to use the energy method to capture the growth of the semi-group and obtain its lower bound, especially if the growth is a transient growth. In this talk, I will present a new energy method to study the lower bound of the semi-group generated by a time-dependent linearized operator. This new energy method gives the growth mechanism of unstable shear flows, with which we prove two open questions about the instability of shear flows for Navier-Stokes and Euler equations. This is a joint work with Nader Masmoudi and Weiren Zhao.
