Axially Symmetric Flow with Finite Cavities I

Abstract

an obstacle is proved. The flow is either in a cylindrical pipe or an unbounded region and the cavity may be finite. The proof is based on a variational approach for a non-continuous func-tional. Essentially is the assumption that the obstacle is starlike with respect to some point on the axis of symmetry. This allows to apply the technique of symmetrization on the stream function.