Stability and non-relativistic limits of rarefaction wave to the 1-D piston problem for the relativistic Euler equations

2017 ◽  
Vol 68 (2) ◽  
Author(s):  
Min Ding ◽  
Yachun Li
Keyword(s):  
Rarefaction Wave ◽  
Euler Equations ◽  
Piston Problem ◽  
Relativistic Euler Equations

Global solution to a three-dimensional spherical piston problem for the relativistic Euler equations

2020 ◽  
pp. 1-26
Author(s):  
LAI GENG
Keyword(s):  
Euler Equations ◽  
Wave Motion ◽  
Surrounding Medium ◽  
Three Dimensional ◽  
Spherically Symmetric ◽  
Piston Problem ◽  
Relativistic Euler Equations ◽  
Symmetric Motion ◽  
Characteristics Method ◽  
Spherically Symmetric Motion

The study of spherically symmetric motion is important for the theory of explosion waves. In this paper, we consider a ‘spherical piston’ problem for the relativistic Euler equations, which describes the wave motion produced by a sphere expanding into an infinite surrounding medium. We use the reflected characteristics method to construct a global piecewise smooth solution with a single shock of this spherical piston problem, provided that the speed of the sphere is a small perturbation of a constant speed.

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
Sign in / Sign up

Export Citation Format

Share Document