Asymptotic Stability of Homogeneous States in the Relativistic Dynamics of Viscous, Heat-Conductive Fluids

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 relativistic fluids. As this second-order system is symmetric hyperbolic, existence and uniqueness on a short time interval follow from the work of Hughes, Kato and Marsden. In this paper 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.