报告题目 (Title)： Asymptotic stability of the three-dimensional Couette flow for the Stokes-transport equations （三维Stokes-transport方程组Couette 流的渐进稳定性）
报告人 (Speaker)：訾瑞昭 教授（华中师范大学）
报告时间 (Time)：2024年10月16日 (周三) 15:00
报告地点 (Place)：腾讯会议： 182-562-357 会议密码：123456
邀请人(Inviter)：厚晓凤
主办部门：8455新葡萄场网站数学系
报告摘要：
In this talk, we investigate the asymptotic stability of the three-dimensional Couette flow in a stratified fluid governed by the Stokes-transport equation. We observe that a similar lift-up effect to the three-dimensional Navier-Stokes equation near Couette flow destabilizes the system, while the inviscid damping type decay due to the Couette flow (Y,0,0) together with the damping structure caused by the decreasing background density $\varrho_{\rm s}(Y)$ stabilizes the system. More precisely, we prove that if the initial density is close to a linearly decreasing function in the Gevrey-1/s class with $1/2<s\leq1$, namely, $\|\varrho_{\rm in}(X,Y,Z)-\varrho_{\rm s}(Y)\|_{\mathcal{G}^{s}}\leq \epsilon$, then the perturbed density remains close to $\varrho_{\rm s}(Y)$. Moreover, the associated velocity field converges to Couette flow (Y, 0, 0) with a convergence rate of 1/(1+t)^3}. This is based on a joint work with Weiren Zhao and Daniel Sinambela.
