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

2025/12/01 by Tao Liang, Jiahong Wu, Liang, Tao +3
Engineering · Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Thin Films #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2512.01159

openalex publication_date 2025/12/01 · openalex created_date 2025/12/03 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the stability threshold of the two-dimensional Boussinesq equations around the Couette flow in an infinite channel ℝ × [-1, 1] under no-slip boundary conditions. We prove that the Couette flow is asymptotically stable under initial perturbations satisfying ‖ vⁱⁿ -(y,0)‖_H² ≤ ε₀ ν^\frac12, and ‖ ρⁱⁿ-1 ‖_H¹ + ‖ |∂_x|^\frac13 ρⁱⁿ ‖_H¹ ≤ ε₁ ν^\frac56. Compared with the work of Masmoudi, Zhai, and Zhao [J. Funct. Anal., 284 (2023), 109736], where the asymptotic stability of the 2D Navier-Stokes-Boussinesq system around Couette flow in a finite channel \mathbbT × [-1, 1] was established, our result improves the stability threshold for the temperature from ν^(11)/(12) to ν^\frac56.

Citations

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Related

• Transition threshold of Couette flow for 2D Boussinesq equations
• Asymptotic stability for two-dimensional Boussinesq systems around the Couette flow in a finite channel
• Stability threshold for two-dimensional Boussinesq systems near-Couette shear flow in a finite channel
• Stability threshold of the Couette flow for Navier-Stokes Boussinesq system with large Richardson number γ²>(1)/(4)
• Stability threshold of Couette flow for Boussinesq equations in ℝ²