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A review is presented of the analytical results available for a large class of axisymmetric stationary flows in the vicinity of compact astrophysical objects. The determination of the two-dimensional structure of the poloidal magnetic field (hydrodynamic flow field) faces severe difficulties, due to the complexity of the trans-field equation for stationary axisymmetric flows. However, an approach exists which enables direct problems to be solved even within the balance law framework. This possibility arises when an exact solution to the equation is available and flows close to it are investigated. As a result, with the use of simple model problems, the basic features of supersonic flows past real compact objects are determined.
Василий С. Бескин (Thu,) studied this question.