A Spatially Localized l log l Estimate on the Vorticity in the 3D NSE

The purpose of this note is to present a spatially localized l log l bound on the vorticity in the 3D Navier-Stokes equations, assuming a very mild, purely geometric condition. This yields an extra-log decay of the distribution function of the vorticity, which in turn implies breaking the criticality in a physically, numerically, and mathematical analysis-motivated criticality scenario based on vortex stretching and anisotropic diffusion.