Thursday, July 5, 2012

1207.1090 (Jussi Lindgren)

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

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.
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