Stability and asymptotic behavior of the 3D Boussinesq equations with MHD convection

This paper is devoted to investigating the stability and large time behavior problem on the three‐dimensional Boussinesq equations for magnetohydrodynamic convection near hydrostatic equilibrium by energy method. The stability for the fluids with certain symmetries is built on the spatial domain with being a 1D period box. In addition, the exponential decay of the oscillation parts is established.