Title: Entropy solutions of the Euler equations for isothermal relativistic fluids

Authors: Philippe G. LeFloch, Mitsuru Yamazaki

Addresses: Laboratoire Jacques-Louis Lions Centre National de la Recherche Scientifique Universite de Paris 6, 4 place Jussieu, 75252 Paris, France. ' Graduate School of Pure and Applied Sciences University of Tsukuba 305-8571 Ibaraki, Japan

Abstract: We investigate the initial-value problem for the relativistic Euler equations of isothermal perfect fluids, and generalise an existence result due to LeFloch and Shelukhin for the non-relativistic setting. We establish the existence of globally defined, bounded measurable, entropy solutions with arbitrary large amplitude. An earlier result by Smoller and Temple covered solutions with bounded variation that avoid the vacuum state. Our new framework provides solutions in a larger function space and allows for the mass density to vanish and the velocity field to approach the light speed. The relativistic Euler equations become strongly degenerate in both regimes, as the conservative or the flux variables vanish or blow up. Our proof is based on the method of compensated compactness and takes advantage of a scaling invariance property of the Euler equations.

Keywords: relativistic Euler equations; isothermal perfect fluids; shock waves; entropy solutions; compensated compactness; non-conservative products; velocity; light speed.

DOI: 10.1504/IJDSDE.2007.013742

International Journal of Dynamical Systems and Differential Equations, 2007 Vol.1 No.1, pp.20 - 37

Published online: 23 May 2007 *

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