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The stability of compressible vortex sheets in two space dimensions. (English) Zbl 1068.35100
The paper deals with vortex sheets, i.e, velocity discontinuities in an inviscid flow, in the compressible case, in two spaces dimensions. An energy estimate for the linearized boundary value problem is proved. Since the problem is characteristic, the estimate 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.

35Q35 PDEs in connection with fluid mechanics
76E17 Interfacial stability and instability in hydrodynamic stability
76B47 Vortex flows for incompressible inviscid fluids
76N15 Gas dynamics (general theory)
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