1207.1090 (Jussi Lindgren)

On the singularity formation, backwards heat equation and
renormalization for the Navier-Stokes equations-A regularity result    [PDF]

Jussi Lindgren

This article models the energy cascade singularity process for the incompressible Navier-Stokes equations. It is shown that the energy density transport in the context of singularity is equivalent to a backwards heat equation. It is then shown through a renormalization type argument that this process leads to a logical contradiction, which shows that such energy cascade singularity process does not exist in the Navier-Stokes equations. This will imply regularity for the Navier-Stokes equations as it is shown that the formation of singularity is developed through a gradient flux of the energy density always.

View original: http://arxiv.org/abs/1207.1090