Couette Flow with Robin Boundary Condition (I): the viscosity-independent friction

2026/07/20 by Siming He, Binqian Niu, Weiren Zhao
#math.AP #math-ph #math.MP

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Abstract

This article is the first paper in the series. In this series of articles, we will examine the influence of the friction factor α at the solid--fluid boundary on the stability of Couette flow. Specifically, we consider the stability of Couette flow in a bounded periodic channel \mathbbT × [-1,1] under Robin-type boundary conditions (u²|_{y=± 1} = 0, [α∂_n u¹ + u¹]|_y=±1 = f ), where α is the friction factor and n is the unit outer normal vector. In this article, we prove that for a given friction factor α, as long as the fluid viscosity coefficient ν≪ α is sufficiently small, the system is asymptotically stable if the initial perturbation satisfies ‖ω_{\rm in}‖ ≤ εν^1/3. Moreover, inviscid damping and enhanced dissipation hold.

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