Nonlinear Stability of Compressible Vortex Sheets

J. -F. Coulombel () and P. Secchi ()
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J. -F. Coulombel: Laboratoire Paul Painlevé
P. Secchi: Facoltà di Ingegneria, Dipartimento di Matematica

A chapter in Hyperbolic Problems: Theory, Numerics, Applications, 2008, pp 415-422 from Springer

Abstract: We present a result on the existence of two-dimensional contact discontinuities solutions to the compressible Euler equations. The problem 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 energy estimates. A similar analysis is applied in the context of weakly stable shock waves and isothermal liquid—vapor phase transitions, and yields analogous existence results.

Keywords: Energy Estimate; Nonlinear Stability; Contact Discontinuity; Vortex Sheet; Compressible Euler Equation (search for similar items in EconPapers)
Date: 2008
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-540-75712-2_38

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DOI: 10.1007/978-3-540-75712-2_38

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