On the stability of the steady states of the gravitating gas disk

The three-dimensional model of the gravitating gas disk, rotating around the gravitating center, is investigated. The numerical algorithm for finding the steady flows in the disk, which uses a solution of the system of nonlinear equations, is built. Density, mass and gravitational potential increase several times in comparison with the model, which does not consider gravity of disk. The parameter Toomre, which determines the stability of steady-state solution, is calculated.