Consistency of some well-posed five-field theories of dissipative relativistic fluid dynamics
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909890525528064 |
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| author | Freistuhler, Heinrich |
| author_facet | Freistuhler, Heinrich |
| contents | Within the FTBDNK family of formulations of relativistic Navier-Stokes (H. Freistühler and B. Temple, Proc. R. Soc. A 470, 20140055 (2014), Proc. R. Soc. A 473 (2017), 20160729; F. S. Bemfica, M. Disconzi, and J. Noronha, Phys. Rev. D 98, 104064 (2018), Phys. Rev. D 100, 104020 (2019); P. Kovtun, J. High Energy Phys. 2019, 034 (2019)), this paper collects some consistency properties for certain causal hyperbolic five-field theories obtained from the Landau-Lifshitz formulation via Eulerian gradient shifts, a family, EGS(L), of models that slightly generalize a class identified in H. Freistühler, J. Math.\ Phys. 61, 033101 (2020). With $ε$ the magnitude of the dissipation coefficients that quantify viscosity and heat conduction, the paper shows that any element of EGS(L) is $O(ε^2)$ equivalent to the Landau-Lifshitz formulation, has an $O(ε^3)$ excess entropy production, represents heterogeneous local thermodynamic equilibria cleanly, and admits regular heteroclinic profiles for all shock waves of sufficiently small amplitude. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_07526 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Consistency of some well-posed five-field theories of dissipative relativistic fluid dynamics Freistuhler, Heinrich Analysis of PDEs Within the FTBDNK family of formulations of relativistic Navier-Stokes (H. Freistühler and B. Temple, Proc. R. Soc. A 470, 20140055 (2014), Proc. R. Soc. A 473 (2017), 20160729; F. S. Bemfica, M. Disconzi, and J. Noronha, Phys. Rev. D 98, 104064 (2018), Phys. Rev. D 100, 104020 (2019); P. Kovtun, J. High Energy Phys. 2019, 034 (2019)), this paper collects some consistency properties for certain causal hyperbolic five-field theories obtained from the Landau-Lifshitz formulation via Eulerian gradient shifts, a family, EGS(L), of models that slightly generalize a class identified in H. Freistühler, J. Math.\ Phys. 61, 033101 (2020). With $ε$ the magnitude of the dissipation coefficients that quantify viscosity and heat conduction, the paper shows that any element of EGS(L) is $O(ε^2)$ equivalent to the Landau-Lifshitz formulation, has an $O(ε^3)$ excess entropy production, represents heterogeneous local thermodynamic equilibria cleanly, and admits regular heteroclinic profiles for all shock waves of sufficiently small amplitude. |
| title | Consistency of some well-posed five-field theories of dissipative relativistic fluid dynamics |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2510.07526 |