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

Nets Hawk Katz·Nataša Pavlović
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Abstract

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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Nets Hawk Katz, Nataša Pavlović. 2001-04-19. A cheap Caffarelli-Kohn-Nirenberg inequality for Navier-Stokes equations with hyper-dissipation. https://arxiv.org/abs/math/0104199

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