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arXiv · 2204.09662

Stability threshold of the Couette flow for Navier-Stokes Boussinesq system with large Richardson number $\gamma^2>\frac{1}{4}$

Cuili Zhai·Weiren Zhao
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Abstract

In this paper, we study the nonlinear asymptotic stability of the Couette flow in the stably stratified regime, namely the Richardson number $\gamma^2>\frac{1}{4}$. Precisely, we prove that if the initial perturbation $(u_{in},\vartheta_{in})$ of the Couette flow $v_s=(y,0)$ and the linear temperature $\rho_s=-\gamma^2y+1$ satisfies $\|u_{in}\|_{H^{s+1}}+\|\vartheta_{in}\|_{H^{s+2}}\leq \epsilon_0\nu^{\frac{1}{2}}$, then the asymptotic stability holds.

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Cuili Zhai, Weiren Zhao. 2022-04-20. Stability threshold of the Couette flow for Navier-Stokes Boussinesq system with large Richardson number $\gamma^2>\frac{1}{4}$. https://arxiv.org/abs/2204.09662

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