# Conservation Laws of the Two-Dimensional Gas Dynamics Equations

## TL;DR

This paper derives conservation laws for two-dimensional gas dynamics equations in mass Lagrangian coordinates, including new laws, using group classification and Noether's theorem, and translates them into Eulerian coordinates.

## Contribution

It introduces new conservation laws for 2D gas dynamics equations and connects Lagrangian and Eulerian formulations using symmetry analysis.

## Key findings

- Derived conservation laws using Noether's theorem.
- Identified new conservation laws in Eulerian coordinates.
- Established correspondence between Lagrangian and Eulerian conservation laws.

## Abstract

Two-dimensional gas dynamics equations in mass Lagrangian coordinates are studied in this paper. The equations describing these flows are reduced to two Euler-Lagrange equations. Using group classification and Noether's theorem, conservation laws are obtained. Their counterparts in Eulerian coordinates are given. Among these counterparts there are new conservation laws.