Abstract
We consider compressible vortex sheets for the isentropic Euler equations of gas dynamics in two space dimensions.Under a supersonic condition that precludes violent instabilities, in previous papers [3, 4] we havestudied the linearized stability and proved the local existence of piecewise smooth solutions to the nonlinearproblem. This is a free boundary nonlinear hyperbolic problem with two main difficulties: the free boundary ischaracteristic, and the so-called Lopatinskii condition holds only in a weak sense, which yields losses ofderivatives. In the present paper we prove that sufficiently smooth solutions are unique.
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