Stability and large time behavior for the 2D BMHD system with partial dissipation and thermal damping

This paper focuses on the Boussinesq equations with magnetohydrodynamics convection in which the temperature obeys degenerate damped wave equations. Under the influence of an equilibrium, we prove that the 2D BMHD system remains stable in the whole space R2. In addition, we obtain the nonlinear large-time behavior and the linear decay rate.