A Prior Derivation and Local Existence of Classical Solutions for the Relativistic Euler Equations with Logarithmic Equation of State

TL;DR

This paper derives a prior formulation of the logarithmic equation of state for relativistic Euler equations and proves the local existence of classical solutions using a symmetric hyperbolic system approach.

Contribution

It introduces a new derivation of the logarithmic equation of state and establishes local existence results for relativistic Euler equations with this state.

Findings

Derivation of the logarithmic equation of state from a symmetric hyperbolic system

Transformation of classical Euler equations into a symmetric hyperbolic form

Proof of local existence of classical solutions for the relativistic Euler equations with the logarithmic state

Abstract

In this paper, from an investigation of a symmetric hyperbolic system, a prior derivation of the logarithm equation of state is provided. Through a diffeomorphism transforming the classical Euler equations to the symmetric hyperbolic system, we show that the logarithm pressure co-exists with existing barotropic equations of state without applying any physical laws. In this connection, we also establish a local existence of classical solutions for the relativistic Euler equations with the logarithm equation of state.