We consider the stationary spatial axisymmetric flow of the viscous incompressible fluid along a semi-infinite needle. It is described by Navier-Stokes system of equations, which is reduced to a system of two partial differential equations. The boundary conditions are set at infinity and at the needle. It's proved that for x → +∞ in boundary layer there is no solution 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