We study the global stability of large solutions to the compressible isentropic magnetohydrodynamic equations in a three-dimensional (3D) bounded domain with Navier-slip boundary conditions. It is shown that the solutions converge to an equilibrium state exponentially in the L²-norm provided the density is essentially uniform-in-time bounded from above. Moreover, we also obtain that the density and magnetic field converge to their equilibrium states exponentially in the L^-norm if additionally the initial density is bounded away from zero. These greatly improve the previous work in (J. Differential Equations 288 (2021), 1-39), where the authors considered the torus case and required the L⁶-norm of the magnetic field to be uniformly bounded as well as zero initial total momentum and an additional restriction 2> for the viscous coefficients. This paper provides the first global stability result for large strong solutions of compressible magnetohydrodynamic equations in 3D general bounded domains.
Liu et al. (Mon,) studied this question.
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