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

How and why non smooth solutions of the 3D Navier-Stokes equations could possibly develop