Communications on Pure and Applied Analysis (CPAA)

Non-relativistic global limits to the three dimensional relativistic euler equations with spherical symmetry

Pages: 365 - 386, Volume 9, Issue 2, March 2010      doi:10.3934/cpaa.2010.9.365

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Xingwen Hao - Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, China (email)
Yachun Li - Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200030, China (email)
Zejun Wang - Department of Mathematics, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China (email)

Abstract: As a fundamental and important step to understand the existence and behavior of solution to the multi-dimensional problem, we study in this paper the three dimensional relativistic Euler equations with spherical symmetry. We obtain the non-relativistic global limits of entropy solutions to the Cauchy problem of the spherically symmetric relativistic Euler equations.

Keywords:  Relativistic Euler equations, spherical symmetry, weak solutions, non-relativistic limits, shock curves, rarefaction wave curves.
Mathematics Subject Classification:  Primary: 35B40, 35A05, 76Y05; Secondary: 35B35, 35L65, 85A05.

Received: May 2009;      Revised: September 2009;      Available Online: December 2009.