  We consider the free boundary problem for non-relativistic and relativistic
ideal compressible magnetohydrodynamics in two and three spatial dimensions
with the total pressure vanishing on the plasma--vacuum interface. We establish
the local-in-time existence and uniqueness of solutions to this nonlinear
characteristic hyperbolic problem under the Rayleigh--Taylor sign condition on
the total pressure. The proof is based on certain tame estimates in anisotropic
Sobolev spaces for the linearized problem and a modification of the Nash--Moser
iteration scheme. Our result is uniform in the light speed and appears to be
the first well-posedness result for the free boundary problem in ideal
compressible magnetohydrodynamics with zero total pressure on the moving
boundary.
