  We prove the local well-posedness in Sobolev spaces of the free-boundary
problem for compressible inviscid resistive isentropic MHD system under the
Rayleigh-Taylor physical sign condition, which describes the motion of a
free-boundary compressible plasma in an electro-magnetic field with magnetic
diffusion. We use Lagrangian coordinates and apply the tangential smoothing
method introduced by Coutand-Shkoller to construct the approximation solutions.
One of the key observations is that the Christodoulou-Lindblad type elliptic
estimate together with magnetic diffusion not only gives the common control of
magnetic field and fluid pressure directly, but also controls the Lorentz force
which is a higher order term in the energy functional.
