Article

Zeitschrift für angewandte Mathematik und Physik ZAMP

, Volume 57, Issue 6, pp 960-983

First online:

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

  • Yachun LiAffiliated withDepartment of Mathematics, Shanghai Jiao Tong University Email author 
  • , Yongcai GengAffiliated withDepartment of Mathematics, Shanghai Jiao Tong University

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Abstract.

We consider in this paper the relativistic Euler equations in isentropic fluids with the equation of state p = κ2ρ, where κ, the sound speed, is a constant less than the speed of light c. We discuss the convergence of the entropy solutions as c→∞. The analysis is based on the geometric properties of nonlinear wave curves and the Glimm’s method.

Mathematics Subject Classification (2000).

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

Keywords.

Isentropic relativistic Euler equations entropy solutions Riemann solutions Glimm’s scheme Lorentz transformation