In this talk, 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 of the fluid is small. Here, we
have no small requirements for the initial velocity and temperature.