1111.0217 (Zoran Grujic)

A geometric measure-type regularity criterion for solutions to the 3D
Navier-Stokes equations    [PDF]

Zoran Grujic

A local geometric measure-type condition on the super-level sets of solutions to the 3D NSE preventing the formation of a finite-time singularity is presented. Although the main utility of this criterion is in ruling out a variety of sparse (both isotropic and anisotropic) blow up scenarios, even in the geometrically amorphous case, the criterion leads to a new critical (scaling-invariant) regularity condition in terms of the decay of the distribution function of a solution.

View original: http://arxiv.org/abs/1111.0217