Generic instabilities in the relativistic Chapman-Enskog heat conduction law
Abstract
We address the well-posedness of the Cauchy problem corresponding to the relativistic first-order fluid equations, coupled with the Chapman-Enskog heat-flux constitutive relation. We show that the system of equations that results by considering linear perturbations with respect to a generic time direction is non-hyperbolic, since there are modes that may arbitrarily grow as wave-number increases. Then, using a result provided by Strang (J Differ Equ 2:107-114, 1966), we conclude that the full non-linear first-order theory is also non-hyperbolic, thus admitting an ill-posed initial-value formulation. Unlike Eckart's theory, these instabilities are not present when the time direction is aligned with the fluid's direction. However, since in general the fluid velocity is not surface-forming, the instability can only be avoided in the particular case where no rotation is present.
- Publication:
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Journal of Statistical Physics
- Pub Date:
- June 2020
- DOI:
- 10.1007/s10955-020-02578-0
- arXiv:
- arXiv:1908.04445
- Bibcode:
- 2020JSP...181..246G
- Keywords:
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- General Relativity and Quantum Cosmology;
- High Energy Physics - Theory
- E-Print:
- 9 pages, 2 figures, refs added