Invariant Plane Steady Isentropic Vortical Gas Flows

Abstract

Elements of group analysis are given for a submodel of plane steady isentropic gas flows. The problem of group classification by arbitrary elements of the equation of state and the values of the Bernoulli and vortex integrals is solved. Optimal systems of subalgebras for two four-dimensional Lie algebras arising in the group classification are constructed. For some cases, the classification of invariant solutions by the optimal system is carried out. Physical interpretation of some solutions is given.