Asymptotic stability in a second-order symmetric hyperbolic system modeling the relativistic dynamics of viscous heat-conductive fluids with diffusion

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2020
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10.1016/j.jde.2019.08.028
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Journal of Differential Equations ; 268 (2020), 2. - pp. 825-851. - Elsevier. - ISSN 0022-0396. - eISSN 1090-2732
Abstract
This paper establishes nonlinear asymptotic stability of homogeneous reference states in dissipative relativistic fluid dynamics. The result is a counterpart for general non-barotropic fluids of one obtained by the author in a previous paper on barotropic fluids. Differently from that of this earlier finding, the proof here crucially relies on analyzing the corresponding linearized problem in Fourier space, with different scalings for small and large wave numbers.
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510 Mathematics
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fluid dynamics, partial differential equations, symmetric hyperbolictiy, quasi-linearity, long-time existence, asymptotic stability
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ISO 690SROCZINSKI, Matthias, 2020. Asymptotic stability in a second-order symmetric hyperbolic system modeling the relativistic dynamics of viscous heat-conductive fluids with diffusion. In: Journal of Differential Equations. Elsevier. 268(2), pp. 825-851. ISSN 0022-0396. eISSN 1090-2732. Available under: doi: 10.1016/j.jde.2019.08.028
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@article{Sroczinski2020-01Asymp-48164,
  year={2020},
  doi={10.1016/j.jde.2019.08.028},
  title={Asymptotic stability in a second-order symmetric hyperbolic system modeling the relativistic dynamics of viscous heat-conductive fluids with diffusion},
  number={2},
  volume={268},
  issn={0022-0396},
  journal={Journal of Differential Equations},
  pages={825--851},
  author={Sroczinski, Matthias}
}
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