Group analysis of three dimensional Euler equations of gas dynamics

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 ${\text{RR}}^4$. Then, an optimal system of one-dimensional sub-algebras for symmetry algebra of this system is given.