The 3D compressible isentropic ideal MHD system with velocity damping on the torus admits unique global smooth solutions near a constant-density equilibrium with uniform background magnetic field satisfying a Diophantine condition, with algebraic decay of perturbations.
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Stabilization by a background magnetic field: global well-posedness of the compressible isentropic ideal MHD equations with velocity damping
The 3D compressible isentropic ideal MHD system with velocity damping on the torus admits unique global smooth solutions near a constant-density equilibrium with uniform background magnetic field satisfying a Diophantine condition, with algebraic decay of perturbations.