  In this paper, we obtain the low order global well-posedness and the
asymptotic behavior of solution of 2D MHD problem with partial dissipation in
half space with non-slip boundary condition. When magnetic field equal zero,
the system be reduced to partial dissipation Navier-Stokes equation, so this
result also implies the stabilizing effects of magnetic field in electrically
conducting fluids. We use the resolvent estimate method to obtain the long time
behavior for the solution of weak diffusion system, which is not necessary to
prove global well-posedness.
