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Uniqueness of 2-D compressible vortex sheets

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  • 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 have studied the linearized stability and proved the local existence of piecewise smooth solutions to the nonlinear problem. This is a free boundary nonlinear hyperbolic problem with two main difficulties: the free boundary is characteristic, and the so-called Lopatinskii condition holds only in a weak sense, which yields losses of derivatives. In the present paper we prove that sufficiently smooth solutions are unique.
    Mathematics Subject Classification: Primary: 76N10; Secondary: 35Q35, 35L50, 76E17.


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