Asymptotic behavior of 2D stably stratified fluids with a damping term in the velocity equation

Thisarticleisconcernedwiththeasymptoticbehaviorofthetwo-dimensionalinviscid Boussinesq equations with a damping term in the velocity equation. Precisely, we provide the time- decay rates of the smooth solutions to that system. The key ingredient is a careful analysis of the Green kernel of the linearized problem in Fourier space, combined with bilinear estimates and interpolation inequalities for handling the nonlinearity.