Internal structure of thin accretion disks

We present analytical results available for a large class of axisymmetric stationary flows in the vicinity of compact astrophysical objects. First, the most general case is formulated corresponding to axisymmetric stationary MHD flows in the Kerr metric. Then, we discuss the hydrodynamical version of the Grad-Shafranov equation. Although not so well-known as the full MHD one, it allows us to clarify the nontrivial structure of the Grad-Shafranov approach as well as to discuss the simplest version of the 3+1-split language - the most convenient one for the description of ideal flows in the vicinity of spinning black holes. Finally, we consider several examples that demonstrate how this approach can be used to obtain the quantitative description of real transonic flows in the vicinity of black holes.