Remarks on sparseness and regularity of Navier-Stokes solutions
Abstract
The goal of this paper is twofold. First, we give a simple proof that sufficiently sparse Navier--Stokes solutions do not develop singularities. This provides an alternative to the approach of Grujic2013, which is based on analyticity and the `harmonic measure maximum principle'. Second, we analyze the claims in algebraicreduction,grujic2019asymptotic that a priori estimates on the sparseness of the vorticity and higher velocity derivatives reduce the 'scaling gap' in the regularity problem.
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