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

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

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