Group analysis of three dimensional Euler equations of gas dynamics

TL;DR

This paper performs symmetry analysis on three-dimensional Euler equations for gas dynamics, deriving similarity reductions, exact solutions, and classifying symmetries to deepen understanding of unsteady gas flows.

Contribution

It provides a comprehensive symmetry analysis, including similarity reductions and classification of sub-algebras, for the 3D Euler equations in gas dynamics.

Findings

Derived similarity reductions and exact solutions.

Classified the symmetry algebra and its sub-algebras.

Established invariance under Galilean transformations.

Abstract

In this paper, the equations governing the unsteady flow of a perfect polytropic gas in three space dimensions are considered. The basic similarity reductions for this system are performed. Reduced equations and exact solutions associated with the symmetries are obtained. This results is used to give the invariance of system up to Galilean motions of space-times $\RR^4$. Then, an optimal system of one-dimensional sub-algebras for symmetry algebra of this system is given.