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2013-07

The interaction of waves for the ultra-relativistic Euler equations

by Mahmoud A.E. Abdelrahman, Matthias Kunik.


Series: 2013-07, Preprints

MSC:
35L45 Initial value problems for first-order hyperbolic systems
35L60 Nonlinear first-order hyperbolic equations
35L65 Conservation laws
35L67 Shocks and singularities
76Y05 Quantum hydrodynamics and relativistic hydrodynamics

Abstract:
We study the interactions between nonlinear waves
for the ultra-relativistic Euler equations for an ideal gas.
These equations are described in terms of the pressure $p$ and
the spatial part $textbf{u} in mathbb{R}^3$ of the dimensionless four-velocity.
We present a new function, which measures the strengths of
the waves of the ultra-relativistic Euler equations, and derive sharp
estimates for these strengths.
We also give the interpretation of the strength for the Riemann
solution. This function has the important implication that
the strength is non increasing for the interactions
of waves for our system. This study of interaction estimates also allows us to determine the type of the outgoing Riemann solutions.

Keywords:
Relativistic Euler equations, conservation laws, hyperbolic systems, shock interaction

This paper was published in:
Journal of Mathematical Analysis and Applications, 2014|409|2|1140-1158.