Stability threshold for 2D shear flows near Couette of the Navier-Stokes equation

2022/03/27 by Dongfen Bian, Bian, Dongfen, Xueke Pu +1
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2203.14332

openalex publication_date 2022/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the stability threshold of the 2D shear flow (U(y),0)^\top of the Navier-Stokes equation at high Reynolds number Re. When the shear flow is near in Sobolev norm to the Couette flow (y,0)^\top in some sense, we prove that if the initial data u₀ satisfies ‖u₀-(U(y),0)^\top‖≤ εRe^-1/3, then the solution of the 2D Navier-Stokes equation approaches to some shear flow which is also close to the Couette flow for t≫ Re^1/3, as t→∞.

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