Generic instabilities in the relativistic Chapman–Enskog heat conduction law

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. Fil: García-Perciante, Ana L.. Universidad Autonoma Metropolitana. Division de Ciencias Sociales y Humanidades. Departamento de Humanidades.; México Fil: Rubio, Marcelo Enrique. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Astronomía Teórica y Experimental. Universidad Nacional de Córdoba. Observatorio Astronómico de Córdoba. Instituto de Astronomía Teórica y Experimental; Argentina