Stability of hydrostatic equilibrium for the 2D magnetic Benard fluid equations with mixed partial dissipation, magnetic diffusion and thermal diffusivity

In mathematics and physics, the problem of the stability of perturbations near the hydrostatic balance is very important. Due to the classical tools designed for the fully dissipated systems are no longer apply, stability and global regularity problems on partially dissipated magnetic Benard fluid equations can be extremely challenging. This paper considers the stability problem on perturbations near the hydrostatic equilibrium for the 2D magnetic Benard fluid equations. We establish the global H-1-stability of the 2D magnetic Benard fluid equations with mixed partial dissipation, magnetic diffusion and thermal diffusivity and affirm the global stability in the Sobolev space H-1 setting.