On three-dimensional numerical modelling hydrodynamic and gravitational instability of the protoplanetary disk

The three-dimensional gas-dynamic model of a proto-planet disk that rotates around a gravitational center is investigated. The dynamics of small perturbations in a rotational shear flow is modeled. The development of initial perturbations of the rotation speed leads to the formation of spiral arms of density and fragmentation of the disk. The results obtained are of interest for the theory of formation of proto-planet systems.