Vortex stretching and anisotropic diffusion in the 3D Navier-Stokes equations
Abstract
The goal of this article is to present -- in a cohesive, and somewhat self-contained fashion -- several recent results revealing an experimentally, numerically, and mathematical analysis-supported \emph{geometric scenario} manifesting \emph{large data} logarithmic \emph{sub-criticality} of the 3D Navier-Stokes regularity problem. Shortly -- in this scenario -- the \emph{transversal small scales} produced by the mechanism of vortex stretching (coupled with the decay of the volume of the regions of intense vorticity) reach the threshold sufficient for the \emph{locally anisotropic diffusion} to engage and control the sup-norm of the vorticity, preventing the (possible) formation of finite time singularities.
Cite
@article{arxiv.1405.3498,
title = {Vortex stretching and anisotropic diffusion in the 3D Navier-Stokes equations},
author = {Zoran Grujić},
journal= {arXiv preprint arXiv:1405.3498},
year = {2014}
}
Comments
final version -- to appear in an issue of Contemporary Mathematics dedicated to the occasion of Hugo Beirao da Veiga's 70th birthday