An axisymmetric boundary layer on a needle
A. D. Bryuno, T V Shadrina · Transactions of the Moscow Mathematical Society · 2007
Methods of power geometry are used to study the boundary layer on a semi-infinite needle, due to a steady flow of a viscous fluid or gas parallel to the needle. The purpose is to find the asymptotics of the flow in the boundary layer at infinity along the needle. Two variants of the flow are considered: (a) an incompressible non-heat-conducting fluid, and (b) a compressible heat-conducting gas. It is shown that variant (a) has no asymptotics for solutions satisfying all the boundary conditions, whereas variant (b) has several families of asymptotics for solutions that satisfy all the boundary conditions. These asymptotic expansions have power or logarithmic singularities near the needle.