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

Authors: Zoran Grujic and Zachary Bradshaw

Issue: Volume 64 (2015), Issue 2, 433-440


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.