A spatially localized $L \\log L$ estimate on the vorticity in the 3D NSE Zachary BradshawZoran Grujic 35763D Navier-Stokescriticalityvorticity 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, \emph{purely geometric} condition. This yields an extra-log decay of the distribution function of the vorticity, which in turn implies \emph{breaking the criticality} in a physically, numerically, and mathematical analysis-motivated criticality scenario based on vortex stretching and anisotropic diffusion. Indiana University Mathematics Journal 2015 text pdf 10.1512/iumj.2015.64.5496 10.1512/iumj.2015.64.5496 en Indiana Univ. Math. J. 64 (2015) 433 - 440 state-of-the-art mathematics http://iumj.org/access/