Vortex stretching and anisotropic diffusion in the 3D Navier-Stokes equations

摘要

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 geometric scenario manifesting large data logarithmic sub-criticality of the 3D Navier-Stokes regularity problem. Shortly - in this scenario - the 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 locally anisotropic diffusion to engage and control the sup-norm of the vorticity, preventing the (possible) formation of finite time singularities.