Conservation Laws of One-Dimensional Equations of Relativistic Gas Dynamics in Lagrangian Coordinates

TL;DR

This paper analyzes one-dimensional relativistic gas dynamics equations in Lagrangian coordinates, deriving conservation laws through symmetry analysis and Noether's theorem, and translating these laws into Eulerian coordinates.

Contribution

It introduces a variational formulation of relativistic gas dynamics equations in Lagrangian coordinates and derives new conservation laws using symmetry analysis.

Findings

Derived conservation laws in Lagrangian variables

Translated conservation laws into Eulerian coordinates

Performed complete symmetry analysis of the equations

Abstract

The present paper is focused on the analysis of the one-dimensional relativistic gas dynamics equations. The studied equations are considered in Lagrangian description, making it possible to find a Lagrangian such that the relativistic gas dynamics equations can be rewritten in a variational form. Complete group analysis of the Euler-Lagrange equation is performed. The symmetries found are used to derive conservation laws in Lagrangian variables by means of Noether's theorem. The analogs of the newly found conservation laws in Eulerian coordinates are presented as well.