报告题目：Asymptotic Stability of Shear Flows Near Couette with Navier Boundary Conditions

报 告 人：王飞副教授（上海交通大学）

报告时间：2024年12月22日下午14:0-15:00

报告地点：龙洞校区行政楼607

主  持  人：翟小平

Abstract: 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.

报告人简介：王飞博士，上海交通大学副教授。2012-2017 南加州大学，博士， 2017-2020 马里兰大学，博士后。 王飞博士在边界层理论，不可压缩流体稳定性及可压缩流体适定性方面都做出了非常有影响力的研究成果，在国际知名杂志如 Adv. Math， Arch. Ration. Mech. Anal.上发表多篇论文。