Relativistic RET of Rarefied Monatomic Gas

In this chapter, firstly, the relativistic Euler model of a gas is presented with the proof that the system is symmetric hyperbolic for general constitutive equations. In the case of rarefied monatomic gas, by using the relativistic Boltzmann-Chernikov equation, appropriate constitutive equations and, in particular, the Synge energy are discussed. The two limits in classical and ultra-relativistic cases are also studied. Then, the modern approach to a relativistic gas with dissipation, that is, RET of a relativistic gas given by Liu, Müller, and Ruggeri (LMR) is summarized. The LMR theory is an improvement to the previous casual theories of Müller and Israel. The RET with many moments, say N moments, is also studied together with the evaluation of the characteristic velocities for increasing number N. In this framework, the maximum characteristic velocity is bounded for any number N. It converges to the light velocity from below when N →∞. In the last section, the classical limit is studied. Then it is proved that, for a fixed N, there exists a unique choice of the moments in classical case. This is probably an answer to the longstanding problem about the optimal choice of moments in the classical case.