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

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

2001-04-19

arxiv.org/abs/math/0104199v1

Mathematics

Analysis of PDEs

24 pages, no figures

Scientific paper

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.

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