# zbMATH — the first resource for mathematics

Symmetries and solutions to equations of two-dimensional motions of polytropic gas. (Russian. English summary) Zbl 1150.76464
Summary: The optimal system of subalgebras for the 9-dimensional Lie algebra is constructed. This system classifies invariant submodels of equation governing the motion of polytropic gas with polytrope-exponent $$\gamma = 2$$. Invariant submodels of rank equal to 0 are found and their physical properties are described.

##### MSC:
 76M60 Symmetry analysis, Lie group and Lie algebra methods applied to problems in fluid mechanics 76N15 Gas dynamics, general 34A05 Explicit solutions, first integrals of ordinary differential equations
Full Text: