Asymptotic Stability of Shear Flows Near Couette with Navier Boundary Conditions
数学专题报告
报告题目(Title)： Asymptotic Stability of Shear Flows Near Couette with Navier Boundary Conditions
报告人(Speaker)：王飞 教授（上海交通大学）
地点(Place)：教三101教室
时间(Time)：2024年6月19日，上午9:00-9:50
邀请人(Inviter)：许孝精
报告摘要
We consider the 2D, incompressible Navier-Stokes equations near the Couette flow, $\omega^{(NS)} = 1 + \eps \omega$, set on the channel $\mathbb{T} \times [-1, 1]$, supplemented with Navier boundary conditions on the perturbation, $\omega|_{y = \pm 1} = 0$. We are simultaneously interested in two asymptotic regimes that are classical in hydrodynamic stability: the long time, $t \rightarrow \infty$, stability of background shear flows, and the inviscid limit, $\nu \rightarrow 0$ in the presence of boundaries. Given small ($\eps \ll 1$, but independent of $\nu$) Gevrey 2- datum, $\omega_0^{(\nu)}(x, y)$, that is supported away from the boundaries $y = \pm 1.
This is the first nonlinear asymptotic stability result of its type, which combines three important physical phenomena at the nonlinear level: inviscid damping, enhanced dissipation, and long-time inviscid limit in the presence of boundaries.
