December  2006, 5(4): 963-979. doi: 10.3934/cpaa.2006.5.963

Non-relativistic global limits of the entropy solutions to the relativistic Euler equations with $\gamma$-law

1. 

Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200030

2. 

Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China

Received  January 2006 Revised  May 2006 Published  September 2006

We analyze the limit as the speed of light $c\rightarrow\infty$ of the global entropy solutions of the $2\times 2$ relativistic Euler equations for the state $p=\kappa^2\rho^\gamma$ $( 1<\gamma<2 )$, and find that the limit is the entropy solution of the corresponding non-relativistic Euler equations.
Citation: Yachun Li, Xucai Ren. Non-relativistic global limits of the entropy solutions to the relativistic Euler equations with $\gamma$-law. Communications on Pure and Applied Analysis, 2006, 5 (4) : 963-979. doi: 10.3934/cpaa.2006.5.963
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