English

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

Analysis of PDEs 2014-02-10 v5

Abstract

The purpose of this note is to present a spatially localized LlogLL \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.

Keywords

Cite

@article{arxiv.1309.2519,
  title  = {A spatially localized $L \log L$ estimate on the vorticity in the 3D NSE},
  author = {Z. Bradshaw and Z. Grujić},
  journal= {arXiv preprint arXiv:1309.2519},
  year   = {2014}
}

Comments

final version; to appear in IUMJ