  Duschl et al. (2000) have shown that the standard model for geometrically
thin accretion disks ($\alpha$-disks) leads to inconsistency if self-gravity
play a role. This problem arise from parametrization of viscosity in terms of
local sound velocity and vertical disks scale hight. The $\beta$-viscosity
prescription was introduced by Duschl et al. (2000), which has been derived
from rotating shear flow experiment ($\nu=\beta \Omega R^2$). Following the
Duschl et al. (2000) suggestion for a $\beta$-prescription for viscosity, we
apply this model for a thin self-gravitating disk around newborn stars. Our
result is quite different with standard alpha disks in the outer part of the
disks where the self-gravity becomes important. In the inner part of the disks,
our solution converged to the standard $\alpha$ disks. It has been presented
that for beta model, Toomre parameter is more than unity everywhere which means
that gravitational fragmentation can be occur everywhere. We suggest that the
kind of hydrodynamically driven viscosity, $\beta$-model, can be used for
modeling of accretion disks from proto-stellar disks to AGN and galactic disks.
It would be interest to investigate ADAF-type solution for follow any effects
by $\beta$-viscosity model. An important property of the $\beta$-disk is that
they are viscously stable.
