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.