Stability threshold of Couette flow for 3D Boussinesq system in Sobolev spaces

2025/04/23 by Shikun Cui, Lili Wang, Cui, Shikun +3 · 2 citations
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2504.16401

openalex publication_date 2025/04/23 · openalex created_date 2025/10/11 · openalex updated_date 2026/07/28

Abstract

In this paper, we investigate the nonlinear stability and transition threshold for the 3D Boussinesq system in Sobolev space under the high Reynolds number and small thermal diffusion in \mathbbT×ℝ×\mathbbT . It is proved that if the initial velocity v_{\rm in} and the initial temperature θ_{\rm in} satisfy ‖v_{\rm in}-(y,0,0)‖_H²≤ εν, ‖θ_{\rm in}‖_H²≤ εν² , respectively for some ε>0 independent of the Reynolds number or thermal diffusion, then the solutions of 3D Boussinesq system are global in time.

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• Stability threshold of the 2D Boussinesq system near Couette flow in an infinite channel
• Inertial instability of Couette flow with Coriolis force

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