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The purpose of this note is to present a spatially localized $L \log L$ boundon the vorticity in the 3D Navier-Stokes equations, assuming a very mild,\emph{purely geometric} condition. This yields an extra-log decay of thedistribution function of the vorticity, which in turn implies \emph{breakingthe criticality} in a physically, numerically, and mathematicalanalysis-motivated blow-up scenario based on vortex stretching and anisotropicdiffusion.

A spatially localized $L \log L$ estimate on the vorticity in the 3D NSE