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

الأصل · EN

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 Lᵖ with respect to small L¹∩ H³ perturbations, 2≤ p≤ ∞. Our analysis follows the approach introduced in [MZ.1] to treat stability of relaxation profiles.