Similarity solutions for three dimensional Euler equations using Lie group analysis

A similarity analysis of the nonlinear three dimensional unsteady Euler equations of gas dynamics is presented using Lie group of transformations with commuting infinitesimal operators. Symmetry groups admitted by the governing system of partial differential equations (PDEs) are obtained, and the complete Lie algebra of infinitesimal symmetries is established. The symmetry generators are used for constructing similarity variables which lead to a reduced system of equations with one independent variable less at each step and eventually to a system of ordinary differential equations (ODEs); in some cases, it is possible to solve these equations exactly.