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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.

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
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