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

Abstract

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.