Asymptotic stability to semi-stationary Boussinesq equations without thermal conduction

Abstract

We study the stability problem of steady solutions to the semi-stationary Boussinesq equations in the strip domain R2×(0,1). For an equilibrium state with any general steady solution θe which satisfies ϑe > m > 0, we show the global existence and asymptotic behavior of solutions to the system with the no-slip boundary condition when the initial temperature is close enough to it. Thus such a steady solution is asymptotically stable, which reflects the well-known phenomenon of Rayleigh-Taylor stability.