The 3D isentropic compressible ideal MHD system with velocity damping admits unique global smooth solutions with algebraic decay near the constant-density equilibrium with uniform background magnetic field satisfying a Diophantine condition.
Kawashima,Smooth global solutions for two-dimensional equations of electromagneto-fluid dynamics,Jpn
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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 isentropic compressible ideal MHD system with velocity damping admits unique global smooth solutions with algebraic decay near the constant-density equilibrium with uniform background magnetic field satisfying a Diophantine condition.