Stability and large time decay for the 3D anisotropic MHD-Boussinesq equations near the hydrostatic equilibrium

This paper investigates the three-dimensional anisotropic magnetohydrodynamics-Boussinesq equations with horizontal fractional dissipation for perturbations around the hydrostatic equilibrium. By thoroughly leveraging the system’s inherent structure, energy-based approaches, and bootstrapping argument techniques, we demonstrate the global stability of the system and the decay rates induced by sufficiently small initial data.