  In this paper, we prove local existence and uniqueness for the 2D
Prandtl-Hartmann regine in weighted Sobolev spaces. Our proof is based on using
uniform estimates of the regularized parabolic equation and maximal principle
under the Oleinik's monotonicity assumption. Compared with Nash-Moser iteration
in \cite{[5]}, the data do not require high regularity.
