Preprint 2003-057

Stability of Large-Amplitude Viscous Shock Profiles of Hyperbolic-Parabolic Systems

Corrado Mascia and Kevin Zumbrun

Abstract: We establish nonlinear $L^1\cap H^3\to L^p$ orbital stability, $2\le p\le \infty$, with sharp rates of decay, of large-amplitude Lax-type shock profiles for a class of symmetric hyperbolic-parabolic systems including compressible gas- and magneto-hydrodynamics (MHD) under the necessary conditions of strong spectral stability, i.e., stable point spectrum of the linearized operator about the wave, transversality of the profile, and hyperbolic stability of the associated ideal shock. This yields in particular, together with the spectral stability results of [MN], the nonlinear stability of arbitrarily large-amplitude shock profiles of isentropic Navier-Stokes equations for a gamma-law gas as $\gamma\to 1$: the first complete large-amplitude stability result for a shock profile of a system with real (i.e. partial) viscosity.

Available as Postscript (168 Kbytes) or gzipped PostScript (424 Kbytes; uncompress using gunzip).
Corrado Mascia, <>
Kevin Zumbrun, <>
Publishing information:
in press in Archive for Rational Mechanics and Analysis
Submitted by:
<> September 10 2003.

[ 1996 | 1997 | 1998 | 1999 | 2000 | 2001 | 2002 | 2003 | All Preprints | Preprint Server Homepage ]
© The copyright for the following documents lies with the authors. Copies of these documents made by electronic or mechanical means including information storage and retrieval systems, may only be employed for personal use.

Conservation Laws Preprint Server <>
Last modified: Thu Sep 11 13:15:37 MEST 2003