Stability threshold for two-dimensional Boussinesq systems near-Couette shear flow in a finite channel

2025/04/03 by Tao Liang, Yongsheng Li, Liang, Tao +3 · 1 citation
Computer Science · Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Nonlinear Dynamics and Pattern Formation

paper · pdf · doi:10.48550/arxiv.2504.02669

openalex publication_date 2025/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the stability threshold problem of the two-dimensional Navier-Stokes Boussinesq(NSB) equations in a finite channel \T × [-1,1], focusing on the stability around the near Couette shear flow (U(y), 0), assuming the Navier slip boundary conditions are satisfied. In particular, when the initial data for the vorticity resides in an anisotropic Sobolev space of size O(min \ μ^(1)/(2), ν^(1)/(2)\), and the initial perturbation of the temperature resides in an anisotropic Sobolev space of size O(min \ μ, ν\), we derive the nonlinear enhanced dissipation effect and the inviscid damping effect for the NSB system.

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• Stability threshold of the 2D Boussinesq system near Couette flow in an infinite channel

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