Lecturer: Zi Ruizhao

Abstract:Consider the linear stability of the three dimensional isentropic compressible Navier-Stokes equations on $\mathbb{T}\times\mathbb{R}\times\mathbb{T}$. We prove the enhanced dissipation phenomenon for the linearized isentropic compressible Navier-Stokes equations around the Couette flow $(y, 0, 0)^\top$. Moreover, the lift-up phenomenon is also shown in this paper. Compared with the 3D incompressible Navier-Stokes equations [Ann. of Math., 185(2017), 541--608], the lift-up effect here is stronger due to the loss of the incompressible condition. This is based on a jointwork with Lan Zeng and Zhifei Zhang.

Introduction to the Lecturer:Zi Ruizhao is an associate professor, master tutor and one of the first "Guizi Young Scholars" of Central China Normal University. He is mainly engaged in the research of well-posedness and stability of solutions of partial differential equations in fluids. He has published over 20 papers in journals such as Archive for Rational Mechanics and Analysis, Mathematische Annalen, Journal of Functional Analysis, Annales de l'Institut Henri Poincaré–Analyse non linéaire, SIAM Journal on Mathematical Analysis, Nonlinearity, Journal of Differ ential Equations. He has successively presided over one project of the Young Scientists Fund and one General Program of the National Natural Science Foundation of China.

Invitee:Tao Tao, Professor from School of Mathematics

Time:14:30-15:30, September 16 (Thursday)

Venue:Tencent Meeting ID: 522 189 159

Hosted by the School of Mathematics, Shandong University