  It is a simple consequence of the Cafarelli-Kohn-Nirenberg theory that every
possible singularity in a thin Haussdorff-measurable set of a Leray- Hopf
solution of the incompressible Navier Stokes equation is on the tip of a small
open cone, where the solution is smooth. Using global regularity results for
weak Hopf-Leray solutions this potential singularity can be analyzed by
investigation of the asymptotic behavior at infinite time of a solution of a
related initial-boundary value problem posed in transformed coordinates on a
cylinder. Next to some new consequences such as global regularity of the Leray
Hopf solution after finite time, many known results can be recovered with this
method succinctly, especially the result that H1-regularity implies global
existence and smoothness.
