This analysis shows global stability and decay rates in magnetohydrodynamics equations, indicating conditions for stability around 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.
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Xiao Li (2025) studied this question.
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