The stability and existence of compressible vortex sheets is studied for two-dimensional isentropic elastic flows. This problem has a free boundary with extra difficulties that the boundary is characteristic and the Kreiss-Lopatinskii condition holds only in a weak sense. A necessary and sufficient condition is obtained for the linear stability of the rectilinear vortex sheets. More precisely, it is shown that, besides the stable supersonic zone, the elasticity exerts an additional stable subsonic zone. Moreover we also obtain the linear stability of the variable states and the local in time existence of the vortex sheets near the stable rectilinear vortex sheets. ududFor the linear stability, we employ the Fourier transform and para-differential calculus to perform the spectrum analysis. Since only the weak Kreiss-Lopatinskii condition holds, the a priori estimates for the linearized system exhibit the loss of derivatives. Thus the existence of vortex sheets is proved by a suitable variation of Nash-Moser iteration scheme.
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