Bounded solutions to the axially symmetric Navier Stokes equation in a cusp region

A domain in R3 that touches the x3 axis at one point is found with following property. For any initial value a C2 class, axially symmetric Navier Stokes equations slip boundary condition have finite energy solution stays bounded for given time, i.e. no time blow up of fluid velocity occurs. The result seems to be first case where Navier-Stokes regularity problem solved beyond dimension 2.