Theoretical basis of the method of successive approximations for stationary problems of the mechanics of a viscous fluid with free separation boundaries

One considers problems with free separation boundaries for flows of a viscous incompressible fluid, described by a complete system of Navier–Stokes equations. One presents a scheme for the construction of approximate methods, giving the possibility to obtain the foundation of energy-type estimates. These schemes are constructed on the basis of a priori estimates, obtained previously at the proof of existence and uniqueness theorems.