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

Yachun Li; Xucai Ren

doi:10.3934/cpaa.2006.5.963

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2006, Volume 5, Issue 4: 963-979. Doi: 10.3934/cpaa.2006.5.963

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

Yachun Li^1, and
Xucai Ren^2,

1.
Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200030
2.
Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240

Received: December 31, 2005

Revised: April 30, 2006

Published: November 2006

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Abstract

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.

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

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