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arXiv · 1908.04445

Generic instabilities in the relativistic Chapman-Enskog heat conduction law

A. L. Garcia-Perciante·Marcelo E. Rubio·Oscar A. Reula
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Abstract

We address the well-posedness of the Cauchy problem corresponding to the relativistic fluid equations, when coupled with the heat-flux constitutive relation arising within the relativistic Chapman-Enskog procedure. The resulting system of equations is shown to be non hyperbolic, by considering general perturbations over the whole set of equations written with respect to a generic time direction. The obtained eigenvalues are not purely imaginary and their real part grows without bound as the wave-number increases. Unlike Eckart's theory, this instability is 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.

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A. L. Garcia-Perciante, Marcelo E. Rubio, Oscar A. Reula. 2019-08-13. Generic instabilities in the relativistic Chapman-Enskog heat conduction law. https://doi.org/10.1007/s10955-020-02578-0

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