Methods of a study of the boundary layer on a needle

Here we explain some ideas and results of Power Geometry, which are used for a study of the axisymmetric boundary layer on a needle. The spatial Power Geometry gives methods for selecting and reducing truncated system of equations, which solutions give a strong asymptotics for solutions to the original system of equations. The planar Power Geometry gives methods for receiving both asymptotics and asymptotic expansions of solutions. In some cases these expansions converge and give the solutions themselves.