Group analysis of three dimensional Euler equations of gas dynamics

2009/08/25 by Mehdi Nadjafikhah, Nadjafikhah, Mehdi
Earth and Planetary Sciences · Environmental Science · Mathematics · #35C05 #76M60 #Analysis of PDEs (math.AP) #Aquatic and Environmental Studies #Differential Geometry (math.DG) #FOS: Mathematics #Gas Dynamics and Kinetic Theory #Methane Hydrates and Related Phenomena

paper · pdf · doi:10.48550/arxiv.0908.3598

openalex publication_date 2009/08/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 \RR⁴. Then, an optimal system of one-dimensional sub-algebras for symmetry algebra of this system is given.

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