Abstract
AbstractCombining pointwise Green's function bounds obtained in a companion paper [36] with earlier, spectral stability results obtained in [16], we establish nonlinear orbital stability of small‐amplitude Lax‐type viscous shock profiles for the class of dissipative symmetric hyperbolic‐parabolic systems identified by Kawashima [20], notably including compressible Navier‐Stokes equations and the equations of magnetohydrodynamics, obtaining sharp rates of decay in Lp with respect to small L1 ∩ H3 perturbations, 2 ≤ p ≤ ∞. Our analysis extends and somewhat refines the approach introduced in [35] to treat stability of relaxation profiles. © 2004 Wiley Periodicals, Inc.
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