the thin plastic layer; the boundary value problem; a free flow in the plane.

In the middle of last century A.Iljushin suggested an efficient two-dimentional, averaged on the layer thickness, mathematical theory of the thin plastic layer flow between two converging rigid plates, formulated the boundary-value problem for «viscous fluid» regarding three unknown functions, two components of velocity and contact pressure. Besides he pointed out the possibility of simplification of the formulation of boundary-value problem till the flow for «ideal fluid». It should be noted, that all successive researchers used the same approach. The flows of plastic layer, which are impossible to describe with the help of «ideal fluid» model, are being considered. For their correct description it is necessary to use the model of «viscous fluid», or the simplified theory of boundary layer, which for indicated proplems is developed in the works of the author.

Kadimov Vagid Ahmedovich, e-mail: vkadymov@yandex.ru, Dr. Sci. Phys. & Math., Professor, Moscow State University of Humanities and Economics, Moscow, Russia