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 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.
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Communicated by T.-P. Liu
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Sroczinski, M. Asymptotic Stability of Homogeneous States in the Relativistic Dynamics of Viscous, Heat-Conductive Fluids. Arch Rational Mech Anal 231, 91–113 (2019). https://doi.org/10.1007/s00205-018-1274-9
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DOI: https://doi.org/10.1007/s00205-018-1274-9