Global existence of the entropy solutions to the isentropic relativistic Euler equations

Yachun Li; Qiufang Shi

doi:10.3934/cpaa.2005.4.763

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2005, Volume 4, Issue 4: 763-778. Doi: 10.3934/cpaa.2005.4.763

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Global existence of the entropy solutions to the isentropic relativistic Euler equations

Yachun Li^1, and
Qiufang Shi^1,

1.
Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200030

Received: January 2005

Revised: May 2005

Published: December 2005

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Abstract

We study the relativistic Euler equations for isentropic fluids with a general equation of state $p=p(\rho)$ satisfying the genuine nonlinearity condition. For the $\gamma$-law case $(1<\gamma<2)$, we establish an existence theorem for global entropy solutions to the Cauchy problem using the Glimm difference scheme. For general pressure, the nonlinear elementary waves and Riemann problem are also studied.

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Mathematics Subject Classification: Primary: 35B40, 35A05, 76Y05; Secondary: 35B35, 35L65,85A05.

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