  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.
