Теоретико-групповые решения уравнений газовой динамики, порожденные трехмерными подалгебрами

We study group-theoretical solutions to the dynamic equations of polytropic gas. We give a complete list of invariant and partially invariant solutions generated by $3$-dimensional subalgebras of symmetry Lie algebra $L_{13}$. There are $146$ different invariant solutions, $61$ partially invariant solutions, and $12$ types of barochronic solutions in this list. This result is applicable in gas dynamics, aerodynamics, and physics of atmosphere.