Improved stability threshold of the Two-Dimensional Couette flow for Navier-Stokes-Boussinesq Systems via quasi-linearization

2024/09/24 by Bin Niu, Weiren Zhao, Niu, Binqian +1 · 1 citation
Engineering · #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows

paper · pdf · doi:10.48550/arxiv.2409.16216

openalex publication_date 2024/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we improve the size requirement of the perturbations for the asymptotic stability of the Couette flow in stratified fluids governed by the two-dimensional Navier-Stokes-Boussinesq system. More precisely, the size of perturbed temperature is improved to ν^2/3 from ν^5/6 in the paper of Zhang and Zi [J. Math. Pure. Anal. 179:123-182 (2023)]. The idea is the quasi-linearization. The main system is decomposed into two or more equations: a good equation (might be linear) that carries the regularity and size of the initial data and some quasi-linear and nonlinear equations that contain the nonlinear part, which start from zero initial data.

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