A cheap Caffarelli-Kohn-Nirenberg inequality for Navier-Stokes equations with hyper-dissipation
Nets Hawk Katz, Nataša Pavlović
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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