12-11
The Ultra-Relativistic Euler Equations
Mahmoud A.E. Abdelrahman, M Kunik
Preprint series: 12-11 , Preprints
MSC:
- 35L45 Initial value problems for hyperbolic systems of first-order PDE
- 35L60 Nonlinear first-order PDE of hyperbolic type
- 35L65 Conservation laws
- 35L67 Shocks and singularities, See also {58C27, 76L05}
- 76Y05 Quantum hydrodynamics and relativistic hydrodynamics, See also {83C55, 85A30}
Abstract: We study the ultra relativistic Euler equations for an ideal gas,
which is a system of nonlinear hyperbolic conservation laws.
We first analyze the single shocks and rarefaction waves
and solve the Riemann problem in a constructive way.
Especially we develop an own parametrization for single shocks,
which will be used to derive a new explicit shock interaction formula.
This shock interaction formula plays an important role in the study
of the ultra relativistic Euler equations.
One application will be presented in this paper, namely
the construction of explicit solutions including shock fronts,
which gives an interesting example for the non-backward uniqueness
of our hyperbolic system
Keywords: Relativistic Euler equations, conservation laws, hyperbolic system, Lorentz transformations, shock waves, entropy conditions, rarefaction waves, Riemann solutions
Notes: The first author is supported
by a fellowship from the Egyptian government in the Long Term Mission system,
and the authors gratefully thank for funding of Mahmoud A.E. Abdelrahman
through this PhD program.
Upload: 2013-04-08-04-08
Upload: 2013-04-08