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2009, Volume 8, Issue 4: 1439-1450. Doi: 10.3934/cpaa.2009.8.1439
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Uniqueness of 2-D compressible vortex sheets

  • 1.

    CNRS, Université Lille 1 and Team Project SIMPAF of INRIA Lille Nord Europe, Laboratoire Paul Painlevé, Bâtiment M2, Cité Scientifique, 59655 VILLENEUVE D'ASCQ CEDEX

  • 2.

    Dipartimento di Matematica, Facoltà di Ingegneria, Università di Brescia, Via Valotti, 9, 25133 Brescia

Received:  May 31, 2008
Revised:  October 31, 2008
Published:  June 2009
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    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 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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