  In this paper, we study the well-posedness of boundary layer problems for the
inhomogeneous incompressible magnetohydrodynamics(MHD) equations, which are
derived from the two dimensional density-dependent incompressible MHD
equations.Under the assumption that initial tangential magnetic field is not
zero and density is a small perturbation of the outer constant flow in
supernorm,the local-in-time existence and uniqueness of inhomogeneous
incompressible MHD boundary layer equation are established in weighted Conormal
Sobolev spaces by energy method. As a byproduct, the local-in-time
well-posedness of homogeneous incompressible MHD boundary layer equations with
any large initial data can be obtained.
