  We consider the two-dimensional MHD Boundary layer system without
hydrodynamic viscosity, and establish the existence and uniqueness of solutions
in Sobolev spaces under the assumption that the tangential component of
magnetic fields dominates. This gives a complement to the previous works of
Liu-Xie-Yang [Comm. Pure Appl. Math. 72 (2019)] and Liu-Wang-Xie-Yang [J.
Funct. Anal. 279 (2020)], where the well-posedness theory was established for
the MHD boundary layer systems with both viscosity and resistivity and with
viscosity only, respectively. We use the pseudo-differential calculation, to
overcome a new difficulty arising from the treatment of boundary integrals due
to the absence of the diffusion property for the velocity.
