  Whether or not smooth solutions to the 3D compressible magnetohydrodynamic
(MHD) equations without magnetic diffusion are always global in time remains an
extremely challenging open problem. No global well-posedness or stability
result is currently available for this 3D MHD system in the whole space
$\mathbb R^3$ or the periodic box $\mathbb T^3$ even when the initial data is
small or near a steady-state solution. This paper presents a global existence
and stability result for smooth solutions to this 3D MHD system near any
background magnetic field satisfying a Diophantine condition.
