Evolution model of the self-gravitating gas disk

The model is described by 3d nonstationary gas dynamic equations in Euler's variables in the cylindrical coordinates and by Poisson's equation for the gravitational potential of disk. The known analytical solutions with equilibrium configurations of polytrophic gas, which do not consider self-gravitation, prove to be unstable. The numerical simulation of the initial equilibrium configuration, which considers self-gravitation, is proposed. It is shown that the numerical solution of complete system of equations is quasi-stationary, the disk structure remains, but the configuration differs from the initial one.