  We prove the local-in-time existence of solutions with a contact
discontinuity of the equations of ideal compressible magnetohydrodynamics (MHD)
for 2D planar flows provided that the Rayleigh-Taylor sign condition $[\partial
p/\partial N]<0$ on the jump of the normal derivative of the pressure is
satisfied at each point of the initial discontinuity. MHD contact
discontinuities are characteristic discontinuities with no flow across the
discontinuity for which the pressure, the magnetic field and the velocity are
continuous whereas the density and the entropy may have a jump. This paper is a
natural completion of our previous analysis [Morando A., Trakhinin Y.,
Trebeschi P., J. Differential Equations 258:2531--2571, 2015] where the
well-posedness in Sobolev spaces of the linearized problem was proved under the
Rayleigh-Taylor sign condition satisfied at each point of the unperturbed
discontinuity. The proof of the resolution of the nonlinear problem given in
the present paper follows from a suitable tame a priori estimate in Sobolev
spaces for the linearized equations and a Nash-Moser iteration.
