  This paper focuses on the 3D incompressible magnetohydrodynamic (MHD)
equations with mixed partial dissipation and magnetic diffusion. Our main
result assesses the global stability of perturbations near the steady solution
given by a background magnetic field. The stability problem on the MHD
equations with partial or no dissipation has attracted considerable interests
recently and there are substantial developments. The new stability result
presented here is among the very few stability conclusions currently available
for ideal or partially dissipated MHD equations. As a special consequence of
the techniques introduced in this paper, we obtain the small data global
well-posedness for the 3D incompressible Navier-Stokes equations without
vertical dissipation.
