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We analyze the relativistic Euler equations of conservation laws of baryonnumber and momentum with a general pressure law. The existence ofglobal-in-time bounded entropy solutions for the system is established bydeveloping a compensated compactness framework. The proof relies on a carefulanalysis of the entropy and entropy-flux functions, which are represented bythe fundamental solutions of the entropy and entropy-flux equations for therelativistic Euler equations. Based on the careful entropy analysis, weestablish a compactness framework for sequences of both exact solutions andapproximate solutions of the relativistic Euler equations. Then we constructapproximate solutions via the vanishing viscosity method and employ ourcompactness framework to deduce the global-in-time existence of entropysolutions. The compactness of the solution operator is also established.Finally, we apply our techniques to establish the convergence of the Newtonianlimit from the entropy solutions of the relativistic Euler equations to theclassical Euler equations.

Global Entropy Solutions and Newtonian Limit for the Relativistic Euler Equations