Gas flow in the vicinity of an axisymmetric spike

The study is concerned with the asymptotic behavior of axisymmetric flow in the vicinity of a tapering body. In particular, two classes of problems are examined: supersonic flow with an attached shock wave and flow with a stagnation point at the tip of the body. The first problem is reduced (through linearization with respect to pure conical flow) to an eigenvalue problem, and certain solution properties are identified. The second problem is reduced (by linearizing with respect to rest) to a spectral problem for the Lagrange equation with limited solution.