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

2006 ◽  
Vol 5 (4) ◽  
pp. 963-979 ◽  
Author(s):  
Yachun Li ◽  
◽  
Xucai Ren ◽  
Keyword(s):  
Euler Equations ◽  
Entropy Solutions ◽  
Relativistic Euler Equations ◽  
Gamma Law

scholarly journals A new variation for the relativistic Euler equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Mahmoud A. E. Abdelrahman ◽  
Hanan A. Alkhidhr
Keyword(s):  
Euler Equations ◽  
Nonlinear Waves ◽  
Approximation Scheme ◽  
Strength Function ◽  
Convergent Sequence ◽  
Approximate Solutions ◽  
Large Initial Data ◽  
Initial Value ◽  
Relativistic Euler Equations ◽  
Glimm Scheme

Abstract The Glimm scheme is one of the so famous techniques for getting solutions of the general initial value problem by building a convergent sequence of approximate solutions. The approximation scheme is based on the solution of the Riemann problem. In this paper, we use a new strength function in order to present a new kind of total variation of a solution. Based on this new variation, we use the Glimm scheme to prove the global existence of weak solutions for the nonlinear ultra-relativistic Euler equations for a class of large initial data that involve the interaction of nonlinear waves.

Second-order accurate kinetic schemes for the ultra-relativistic Euler equations

2003 ◽  
Vol 192 (2) ◽  
pp. 695-726 ◽  
Author(s):  
Matthias Kunik ◽  
Shamsul Qamar ◽  
Gerald Warnecke
Keyword(s):  
Euler Equations ◽  
Second Order ◽  
Relativistic Euler Equations ◽  
Kinetic Schemes
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