Non-relativistic global limits of entropy solutions to the extremely relativistic Euler equations

Article

DOI: 10.1007/s00033-009-0031-1

Cite this article as:
Geng, Y. & Li, Y. Z. Angew. Math. Phys. (2010) 61: 201. doi:10.1007/s00033-009-0031-1

Abstract

We are concerned in this paper with the non-relativistic global limits of the entropy solutions to the Cauchy problem of 3 × 3 system of relativistic Euler equations modeling the conservation of baryon numbers, momentum, and energy respectively. Based on the detailed geometric properties of nonlinear wave curves in the phase space and the Glimm’s method, we obtain, for the isothermal flow, the convergence of the entropy solutions to the solutions of the corresponding classical non-relativistic Euler equations as the speed of light c → +∞.

Mathematics Subject Classification (2000)

Primary: 35B40 35A05 76Y05 Secondary: 35B35 35L65 85A05 

Keywords

Relativistic Euler equations Lorentz invariance Newtonian limits Riemann problem Cauchy problem Shocks Rarefaction waves Glimm’s scheme Approximate solutions 

Copyright information

© Birkhäuser Verlag Basel/Switzerland 2009

Authors and Affiliations

  1. 1.Department of MathematicsShanghai Jiao Tong UniversityShanghaiPeople’s Republic of China
  2. 2.Department of MathematicsShanghai Jiao Tong UniversityShanghaiPeople’s Republic of China

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