By methodsof Power Geometry, we study the classical problem of the boundary layer in the viscous incompressible fluid flow around a semi-infinite plate. The flow is described by the Navier--Stocks system of three partial differential equations. When one tends to infinity along the plate, the asymptotics of the flow satisfies to a truncated system, which is reduced in self-similar coordinates to the ordinary differential Blasius equation. A detailed study of its solutions allows to describe the asymptotics of the flow. We give a survey of know results as well. The paper is mostly methodological, but it contains also some new results.

Mathematical problems and theory of numerical methods