  We consider the validity of Prandtl boundary layer expansion of solutions to
the initial boundary value problem for inhomogeneous incompressible
magnetohydrodynamics (MHD) equations in the half plane when both viscosity and
resistivity coefficients tend to zero, where the no-slip boundary condition is
imposed on velocity while the perfectly conducting condition is given on
magnetic field. Since there exist strong boundary layers, the essential
difficulty in establishing the uniform $L^\infty$ estimates of the error
functions comes from the unboundedness of curl of the strong boundary layers.
Under the assumptions that the viscosity and resistivity coefficients take the
same order of a small parameter and the initial tangential magnetic field has a
positive lower bound near the boundary, we prove the validity of Prandtl ansatz
in $L^\infty$ sense in Sobolev framework. Compared with the homogeneous
incompressible case considered in \cite{LXY192}, some suitable functionals
should be designed and the elaborated co-normal energy estimates will be
involved in analysis due to the variation of density and the interaction
between the density and velocity.
