Generic instabilities in the relativistic Chapman-Enskog heat conduction law

GARCÍA-PERCIANTE, ANA L.; REULA, OSCAR A.; RUBIO, MARCELO E.

JOURNAL OF STATISTICAL PHYSICS

SPRINGER

Año: 2020 p. 246 - 262

0022-4715

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.