A cheap Caffarelli-Kohn-Nirenberg inequality for Navier-Stokes equations with hyper-dissipation

Abstract

We prove that for the Navier Stokes equation with dissipation $(-\Delta)^{\alpha}$, where $1<\alpha<{5/4}$, and smooth initial data, the Hausdorff dimension of the singular set at time of first blow up is at most $5-4\alpha$. This unifies two directions from which one might approach the Clay prize problem.