数学科学学院学术报告[2024] 104号

(高水平大学建设系列报告984号)

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11月11日，下午13:30-14:30

报告地点：汇星楼一楼一号教室

报告摘要：We consider the 2D, incompressible Navier-Stokes equations near the Couette flow, $\omega^{(NS)} = 1 + \epsilon \omega$, 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 ($\epsilon \ll 1$, 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，上海交通大学数学科学学院，副教授，博士生导师。主要研究兴趣为流体相关的偏微分方程，具体包括边界层理论，流体稳定性，适定性等方面。研究成果发表在Adv. Math, ARMA, CMP等期刊。

欢迎师生参加！

邀请人：张擎天

数学科学学院

2024年10月24日