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.
Categories: math.AP