A Proposal of a Damping Term for the Relativistic Euler Equations

TL;DR

This paper introduces a damping term for the 3D relativistic Euler equations, demonstrating its consistency with non-relativistic limits and establishing local existence of smooth solutions.

Contribution

It proposes a novel damping term for relativistic Euler equations and formulates them as a symmetric hyperbolic system for mathematical analysis.

Findings

Equations reduce to classical damped Euler equations in the Newtonian limit.

Local-in-time existence of smooth solutions is established.

The damping term maintains physical consistency in the relativistic framework.

Abstract

We introduce a damping term for the special relativistic Euler equations in $3$-D and show that the equations reduce to the non-relativistic damped Euler equations in the Newtonian limit. We then write the equations as a symmetric hyperbolic system for which local-in-time existence of smooth solutions can be shown.