Siberian Federal University

The three-dimensional motion of gas within the limits of model of a stationary special vortex with grav- itation is considered. Using methods of the group analysis of the differential equations, it is possible to reduce studying of properties of the decision to research of properties of an implicitly defined ordinary differential equation. The properties of solutions of this equation are studied, a description of modes of a current in the phase space is obtained, the existence of subsonic and supersonic modes of a gas motion in physical space is proved. It is shown that classification of types of decisions and their qualitative be- havior to a similar case of a vortex of Ovsyannikov without gravitation (A.A.Cherevko, A.P.Chupakhin, 2005).