Publikation: Decay and subluminality of modes of all wave numbers in the relativistic dynamics of viscous and heat conductive fluids
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2021
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Journal of Mathematical Physics. American Institute of Physics (AIP). 2021, 62(5), 053101. ISSN 0022-2488. eISSN 1089-7658. Available under: doi: 10.1063/5.0039351
Zusammenfassung
To further confirm the causality and stability of a second-order hyperbolic system of partial differential equations that models the relativistic dynamics of barotropic fluids with viscosity and heat conduction [H. Freistühler and B. Temple, J. Math. Phys. 59, 063101 (2018)], this paper studies the Fourier–Laplace modes of this system and shows that all such modes, relative to arbitrary Lorentz frames, (a) decay with increasing time and (b) travel at subluminal speeds. Stability is also shown for the related model of non-barotropic fluids [H. Freistühler and B. Temple, Proc. R. Soc. A 470, 20140055 (2014) and H. Freistühler and B. Temple, Proc. R. Soc. A 473, 20160729 (2017)]. Even though these properties had been known for a while in the sense of numerical evidence, the fully analytical proofs for the subluminality of modes of arbitrary wave numbers in arbitrary frames given here appear to be the first regarding any four-field formulation of dissipative relativistic fluid dynamics.
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FREISTÜHLER, Heinrich, Moritz REINTJES, Blake TEMPLE, 2021. Decay and subluminality of modes of all wave numbers in the relativistic dynamics of viscous and heat conductive fluids. In: Journal of Mathematical Physics. American Institute of Physics (AIP). 2021, 62(5), 053101. ISSN 0022-2488. eISSN 1089-7658. Available under: doi: 10.1063/5.0039351BibTex
@article{Freistuhler2021Decay-55526,
year={2021},
doi={10.1063/5.0039351},
title={Decay and subluminality of modes of all wave numbers in the relativistic dynamics of viscous and heat conductive fluids},
number={5},
volume={62},
issn={0022-2488},
journal={Journal of Mathematical Physics},
author={Freistühler, Heinrich and Reintjes, Moritz and Temple, Blake},
note={Article Number: 053101}
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<dcterms:abstract xml:lang="eng">To further confirm the causality and stability of a second-order hyperbolic system of partial differential equations that models the relativistic dynamics of barotropic fluids with viscosity and heat conduction [H. Freistühler and B. Temple, J. Math. Phys. 59, 063101 (2018)], this paper studies the Fourier–Laplace modes of this system and shows that all such modes, relative to arbitrary Lorentz frames, (a) decay with increasing time and (b) travel at subluminal speeds. Stability is also shown for the related model of non-barotropic fluids [H. Freistühler and B. Temple, Proc. R. Soc. A 470, 20140055 (2014) and H. Freistühler and B. Temple, Proc. R. Soc. A 473, 20160729 (2017)]. Even though these properties had been known for a while in the sense of numerical evidence, the fully analytical proofs for the subluminality of modes of arbitrary wave numbers in arbitrary frames given here appear to be the first regarding any four-field formulation of dissipative relativistic fluid dynamics.</dcterms:abstract>
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