  In this paper, we establish the mathematical validity of the Prandtl boundary
layer theory for a class of nonlinear plane parallel flows of viscous
incompressible magnetohydrodynamic (MHD) flow with no-slip boundary condition
of velocity and perfectly conducting wall for magnetic fields. The convergence
is shown under various Sobolev norms, including the physically important
space-time uniform norm $L^\infty(H^1)$. In addition, the similar convergence
results are also obtained under the case with uniform magnetic fields. This
implies the stabilizing effects of magnetic fields. Besides, the higher-order
expansion is also considered.
