Preprint 2003-020

The stability of compressible vortex sheets in two space dimensions

Jean-Francois Coulombel, Paolo Secchi

Abstract: We study the linear stability of planar compressible vortex sheets in two space dimensions. Under a supersonic condition that precludes violent instabilities, we prove an energy estimate for the linearized boundary value problem. Since the problem is characteristic, the estimate we prove exhibits a loss of control on the trace of the solution. Furthermore, the failure of the uniform Kreiss-Lopatinskii condition yields a loss of derivatives in the energy estimate.

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Jean-Francois Coulombel, <>
Paolo Secchi, <>
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<> March 8 2003.

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