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arXiv · 1805.05179

On the asymptotic stability of stratified solutions for the 2D Boussinesq equations with a velocity damping term

Angel Castro·Diego Córdoba·Daniel Lear
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Abstract

We consider the 2D Boussinesq equations with a velocity damping term in a strip $\mathbb{T}\times[-1,1]$, with impermeable walls. In this physical scenario, where the \textit{Boussinesq approximation} is accurate when density/temperature variations are small, our main result is the asymptotic stability for a specific type of perturbations of a stratified solution. To prove this result, we use a suitably weighted energy space combined with linear decay, Duhamel's formula and "bootstrap" arguments.

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Angel Castro, Diego Córdoba, Daniel Lear. 2018-05-11. On the asymptotic stability of stratified solutions for the 2D Boussinesq equations with a velocity damping term. https://arxiv.org/abs/1805.05179

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