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On the transition to instability for compressible vortex sheets

Published online by Cambridge University Press:  12 July 2007

Jean-François Coulombel  and
Paolo Secchi
Jean-François Coulombel
Affiliation:
CNRS and Laboratoire Paul Painlevé, Bâtiment M2, Cité Scientifique, 59655 Villeneuve d'Ascq Cedex, France (jfcoulom@math.univ-lille1.fr)
Paolo Secchi
Affiliation:
Dipartimento di Matematica, Facoltà di Ingegneria, Via Valotti 9, 25123 Brescia, Italy (paolo.secchi@ing.unibs.it)
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Abstract

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We study the linear stability of a vortex sheet in a limit case that corresponds to a transition between a weakly stable regime and a violently unstable regime. We prove an energy estimate that reflects the high degeneracy of the uniform Kreiss–Lopatinskii condition.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 134 , Issue 5 , October 2004 , pp. 885 - 892
Copyright
Copyright © Royal Society of Edinburgh 2004