Global Well-Posedness of an Initial-Boundary Value Problem for Viscous Non-Resistive MHD Systems

This paper concerns the viscous and non-resistive MHD systems which govern the motion of electrically conducting fluids interacting with magnetic fields.We consider an initial-boundary value problem for both compressible and (nonhomogeneous and homogeneous) incompressible fluids in an infinite flat layer.We prove the global well-posedness of the systems around a uniform magnetic field which is vertical to the layer.Moreover, the solution converges to the steady state at an almost exponential rate as time goes to infinity.Our proof relies on a two-tier energy method for the reformulated systems in Lagrangian coordinates.