Abstract
In this paper, we establish the nonlinear stability and large time behavior of hydrostatic equilibrium in a uniform magnetic field for the 2D Boussinesq system with magnetohydrodynamics convection on spatial domain with partial dissipation. This is the important part of further work about the stability/instability of shear flow which is the combination of hydrostatic equilibrium and Couette/shear flow in a uniform magnetic field with partial dissipation.
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