Abstract
We show that when entropy variations are included and special relativity is imposed, the thermodynamics of a perfect fluid leads to two distinct families of equations of state whose relativistic compressible Euler equations are of Nishida type. (In the non-relativistic case there is only one.) The first corresponds exactly to the Stefan-Boltzmann radiation law, and the other, emerges most naturally in the ultra-relativistic limit of a γ-law gas, the limit in which the temperature is very high or the rest mass very small. We clarify how these two relativistic equations of state emerge physically, and provide a unified analysis of entropy variations to prove global existence in one space dimension for the two distinct 3 × 3 relativistic Nishida-type systems. In particular, as far as we know, this provides the first large data global existence result for a relativistic perfect fluid constrained by the Stefan-Boltzmann radiation law.
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Communicated by P. Constantin
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Wissman, B.D. Global Solutions to the Ultra-Relativistic Euler Equations. Commun. Math. Phys. 306, 831–851 (2011). https://doi.org/10.1007/s00220-011-1299-5
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DOI: https://doi.org/10.1007/s00220-011-1299-5