Global existence of classical solutions to the two-dimensional compressible Boussinesq equations in a square domain

Abstract

In this paper, we consider the initial boundary value problem of two-dimensional isentropic compressible Boussinesq equations with constant viscosity and thermal diffusivity in a square domain. Based on the time-independent lower-order and time-dependent higher-order a priori estimates, we prove that the classical solution exists globally in time provided the initial mass $\|\rho _{0}\|_{L^{1}}$ ∥ ρ 0 ∥ L 1 of the fluid is small. Here, we have no small requirements for the initial velocity and temperature.