A model for relativistic fluid mixture with different pressure laws

In the present paper a model for a compressible relativistic fluid 2-component mixture with different temperature, and even different pressure laws, is obtained. Total pressure is then the sum of the two independent pressures, which are supposed to be described by an evolution equation formally analogous to the usual one governing the pressure of a simple fluid. The deduced system is able to describe different complex situations, like plasma physics where the temperature of the electrons must be different from the temperatures of the other species. Weak discontinuities compatible with such kind of mixtures are also studied. In the isentropic case the governing equations are put into symmetric hyperbolic form in which the dependent variables are the two pressures plus a generalized velocity vector defined by the fluid's unit 4-velocity divided pointwise by the fluid's index.