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 blow-up scenario based on vortex stretching and anisotropic diffusion.
Categories: math.AP