勷勤数学•专家报告

题      目：Asymptotic Stability of Shear Flows Near Couette with Navier Boundary Conditions

报  告  人： 王飞 副教授  (邀请人：林植林)

                                       上海交通大学

时      间： 10月21日  14:30-15:30

地     点：数学科学学院西楼111

报告人简介:

        王飞现为上海交通大学数学科学学院副教授。王飞博士毕业于南加州大学，曾在马里兰大学从事博士后研究工作。主要从事边界层理论，不可压缩流体稳定性及可压缩流体适定性等方面的研究，相关研究成果发表于 Adv. Math， Arch. Ration. Mech. Anal., CMP等知名期刊。

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.

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