Asymptotic stability of homogeneous states in the relativistic dynamics of viscous, heat-conductive fluids

Abstract

This paper shows global-in-time existence and asymptotic decay of small solutions to the Navier-Stokes-Fourier equations for a class of viscous, heat-conductive fluids. As this second-order system is symmetric-hyperbolic, existence and uniqueness on a short time interval follow from work of Hughes, Kato, and Marsden. Here it is proven that solutions which are close to a homogeneous reference state can be extended globally and decay to the reference state. The proof combines decay results for the linearization with refined Kawashima-type estimates of the nonlinear terms.