  Fluid configurations in three-dimensions, displaying a plausible decay of
regularity in a finite time, are suitably built and examined. Vortex rings are
the primary ingredients in this study. The full Navier-Stokes system is
converted into a 3D scalar problem, where appropriate numerical methods are
implemented in order to figure out the behavior of the solutions. Further
simplifications in 2D and 1D provide interesting toy problems, that may be used
as a starting platform for a better understanding of blowup phenomena.
