scholarly journals Global solutions of the relativistic Euler equations

1993 ◽  
Vol 156 (1) ◽  
pp. 67-99 ◽  
Author(s):  
Joel Smoller ◽  
Blake Temple
Keyword(s):  
Euler Equations ◽  
Global Solutions ◽  
Relativistic Euler Equations

Global solutions for the ultra-relativistic Euler equations

2017 ◽  
Vol 155 ◽  
pp. 140-162 ◽  
Author(s):  
Mahmoud A.E. Abdelrahman
Keyword(s):  
Euler Equations ◽  
Global Solutions ◽  
Relativistic Euler Equations

scholarly journals Riemann problem with delta initial data for the two-dimensional steady pressureless isentropic relativistic Euler equations

2021 ◽  
Author(s):  
Yu Zhang ◽  
Yanyan Zhang
Keyword(s):  
Initial Data ◽  
Euler Equations ◽  
Riemann Problem ◽  
Contact Discontinuity ◽  
Global Solutions ◽  
Two Dimensional ◽  
Relativistic Euler Equations ◽  
Riemann Solutions ◽  
Isentropic Relativistic Euler Equations ◽  
The Stability

The Riemann problem for the two-dimensional steady pressureless isentropic relativistic Euler equations with delta initial data is studied. First, the perturbed Riemann problem with three pieces constant initial data is solved. Then, via discussing the limits of solutions to the perturbed Riemann problem, the global solutions of Riemann problem with delta initial data are completely constructed under the stability theory of weak solutions. Interestingly, the delta contact discontinuity is found in the Riemann solutions of the two-dimensional steady pressureless isentropic relativistic Euler equations with delta initial data.

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

Two dimensional relativistic Euler equations in a convex duct

2018 ◽  
Vol 461 (2) ◽  
pp. 1084-1099 ◽  
Author(s):  
Liping Luan ◽  
Jianjun Chen ◽  
Jianli Liu
Keyword(s):  
Euler Equations ◽  
Two Dimensional ◽  
Relativistic Euler Equations
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