Abstract
Gravitational instabilities are important to the evolution of the disks and the planet formation in the disks. We calculate the evolution of the disks that form from the collapse of the molecular cloud cores. By changing the properties of the cloud cores and the hydrodynamical viscosity parameters, we explore their effects on the properties of the gravitational instabilities. We find that the disk is unstable when the angular velocity of the molecular cloud core is larger than a critical value. The time duration of the instability increases as the angular velocity of the core increases. The increase of the hydrodynamical viscosity parameter hardly affects the stability of the disk, but decreases the time duration of the critical state of the gravitational instability in the disk. The instability of the disks can happen at very early time of evolution of the disk, which is consistent with the observations.
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