We consider the stationary spatial axisymmetric flow of the viscous compressible heat conductive fluid along a semi-infinite needle. It is described by a system of three partial differential equations with boundary conditions at infinity and on the needle. Its truncated system, describing the flow in the boundary layer, was selected by methods of Power Geometry. In self-similar coordinates this system is reduced to a system of two ordinary differential equations and on its invariant manifold ut was reduced to a second order differential equation. Analysis of solutions of the equation, made by methods of Power Geometry and numerically, shows the existence of families of solutions satisfying all boundary conditions. We used results of our preprint 'Methods of a study of the boundary layer on a needle'.

Mathematical problems and theory of numerical methods