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

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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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Authors and Affiliations

  1. Department of Mathematics, University of Konstanz, 78457, Konstanz, Germany

    Matthias Sroczinski

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  1. Matthias Sroczinski
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Correspondence to Matthias Sroczinski.

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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

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