Симметрии и решения уравнений двумерных движений политропного газа

The optimal system of subalgebras for the $9$-dimensional Lie algebra was 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 $0$ were found and their physical properties were described.