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

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.

40 pages. Revised argument in section 6.2, results unchanged. arXiv admin note: text overlap with arXiv:1804.08490; text overlap with arXiv:1410.1415 by other authors