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arXiv · 2504.02669

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

Tao Liang·Yongsheng Li·Xiaoping Zhai
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Abstract

In this paper, we investigate the stability threshold problem of the two-dimensional Navier-Stokes Boussinesq(NSB) equations in a finite channel $ \T \times [-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 \{ \mu^{\frac{1}{2}}, \nu^{\frac{1}{2}}\})$, and the initial perturbation of the temperature resides in an anisotropic Sobolev space of size $ O(\min \{ \mu, \nu\})$, we derive the nonlinear enhanced dissipation effect and the inviscid damping effect for the NSB system.

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Tao Liang, Yongsheng Li, Xiaoping Zhai. 2025-04-03. Stability threshold for two-dimensional Boussinesq systems near-Couette shear flow in a finite channel. https://arxiv.org/abs/2504.02669

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