Stability of viscous shock profiles for dissipative symmetric hyperbolic-parabolic systems

Details Stability of viscous shock profiles for dissipative symmetric hyperbolic-parabolic systems Stability of viscous shock profiles for dissipative symmetric hyperbolic-parabolic systems

2001-08-03

arxiv.org/abs/math/0108024v1

Mathematics

Analysis of PDEs

Scientific paper

Combining pointwise Green's function bounds obtained in a companion paper [MZ.2] with earlier, spectral stability results obtained in [HuZ], we establish nonlinear orbital stability of small amplitude viscous shock profiles for the class of dissipative symmetric hyperbolic-parabolic systems identified by Kawashima [Kaw], notably including compressible Navier--Stokes equations and the equations of magnetohydrodynamics, obtaining sharp rates of decay in $L^p$ with respect to small $L^1\cap H^3$ perturbations, $2\le p\le \infty$. Our analysis follows the approach introduced in [MZ.1] to treat stability of relaxation profiles.

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