The stability of compressible vortex sheets in two space dimensions

Jean-François Coulombel (1) , Paolo Secchi (2)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 UniBs - Università degli Studi di Brescia = University of Brescia

We study the linear stability of 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.

Domaines: Equations aux dérivées partielles [math.AP]

Jean-François Coulombel, Paolo Secchi. The stability of compressible vortex sheets in two space dimensions. Indiana University Mathematics Journal, 2004, 53 (4), pp.941 - 1012. ⟨10.1512/iumj.2004.53.2526⟩. ⟨hal-01838950⟩