  Axisymmetric accretion disks in vicinity of a central compact body are
studied. For the simple models such as vertically isothermal disks as well as
adiabatic ones the exact solutions to the steady-state MHD
(magneto-hydrodynamic) system were found under the assumption that the radial
components of velocity and magnetic field are negligible. On the basis of the
exact solution one may conclude that vertically isothermal disks will be
totally isothermal. The exact solution for the case of adiabatic disk
corroborates the view that thin disk accretion must be highly non-adiabatic. An
intermediate approach, that is between the above-listed two, for the modeling
of thin accretion disks is developed. In the case of non-magnetic disk, this
approach enables to prove, with ease, that all solutions for the mid-plane
circular velocity are unstable provided the disk is non-viscous. Hence, this
approach enables to demonstrate that the pure hydrodynamic turbulence in
accretion disks is possible. It is interesting that a turbulent magnetic disk
tends to be Keplerian. This can easily be shown by assuming that the turbulent
gas tends to flow with minimal losses, i.e. to have the Euler number as small
as possible.
