TY - JOUR
T1 - Causal dissipation for the relativistic dynamics of ideal gases
JF - Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science
M3 - 10.1098/rspa.2016.0729
VL - 473
IS - 2201
AU - FreistÃ¼hler, Heinrich
AU - Temple, Blake
Y1 - 2017/05/01
UR - http://rspa.royalsocietypublishing.org/content/473/2201/20160729.abstract
N2 - We derive a general class of relativistic dissipation tensors by requiring that, combined with the relativistic Euler equations, they form a second-order system of partial differential equations which is symmetric hyperbolic in a second-order sense when written in the natural Godunov variables that make the Euler equations symmetric hyperbolic in the first-order sense. We show that this class contains a unique element representing a causal formulation of relativistic dissipative fluid dynamics which (i) is equivalent to the classical descriptions by Eckart and Landau to first order in the coefficients of viscosity and heat conduction and (ii) has its signal speeds bounded sharply by the speed of light. Based on these properties, we propose this system as a natural candidate for the relativistic counterpart of the classical Navierâ€“Stokes equations.
ER -