  We are concerned with the vortex sheet solutions for the inviscid two-phase
flow in two dimensions. In particular, the nonlinear stability and existence of
compressible vortex sheet solutions under small perturbations are established
by using a modification of the Nash-Moser iteration technique, where a priori
estimates for the linearized equations have a loss of derivatives. Due to the
jump of the normal derivatives of densities of liquid and gas, we obtain the
normal estimates in the anisotropic Sobolev space, instead of the usual Sobolev
space. New ideas and techniques are developed to close the energy estimates and
derive the tame estimates for the two-phase flows.
