# American Institute of Mathematical Sciences

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