ISSN 2542–0380 
Труды Института механики им. Р.Р. Мавлютова
Электронный научный журнал  Electronic Scientific Journal
Proceedings of the Mavlyutov Institute of Mechanics

We consider the system of gas dynamics equations with the state equation of the monatomic gas. The system admits a group of transformations with a 14dimensional Lie algebra. A projective operator is specific to this algebra. We consider the invariant submodel on twodimensional subalgebra containing the projective operator. For the vorticityfree motions, the submodel is reduced to an overdetermined system of three equations. A particular solution is found for it, physical interpretation is given, and trajectories of gas particles are depicted. The solution gives the gas compression followed by expansion.
monatomic gas,
invariant solution,
vorticityfree motion
Problem: To consider the invariant submodel on twodimensional subalgebra containing a projective operator for the 14dimensional Lie algebra admitted by the equations of motion of the monatomic gas. To consider the condition of vorticityfree motion.
Methods: The methods of the theory of differential equations and group analysis are used.
In a study was determined:
1. For vorticityfree motion, the submodel is reduced to an overdetermined system of three equations.
2. For vorticityfree motion, a particular solution is found and its physical interpretation is given.