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

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December 2005, 4(4): 763-778. doi: 10.3934/cpaa.2005.4.763

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

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

Received January 2005 Revised May 2005 Published September 2005

Abstract
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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.

Keywords: Glimm Scheme, Riemann problem, Lorentz transformation, entropy solutions, isentropic fluids, Relativistic Euler equations.

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

Citation: Yachun Li, Qiufang Shi. Global existence of the entropy solutions to the isentropic relativistic Euler equations. Communications on Pure & Applied Analysis, 2005, 4 (4) : 763-778. doi: 10.3934/cpaa.2005.4.763

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