Remarks on sparseness and regularity of Navier-Stokes solutions
Analysis of PDEs
2022-06-22 v2
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 \cite{Grujic2013}, which is based on analyticity and the `harmonic measure maximum principle'. Second, we analyze the claims in \cite{algebraicreduction,grujic2019asymptotic} that \emph{a priori} estimates on the sparseness of the vorticity and higher velocity derivatives reduce the 'scaling gap' in the regularity problem.
Cite
@article{arxiv.2110.02187,
title = {Remarks on sparseness and regularity of Navier-Stokes solutions},
author = {Dallas Albritton and Zachary Bradshaw},
journal= {arXiv preprint arXiv:2110.02187},
year = {2022}
}
Comments
20 pages, 1 figure. Revised version, to appear in Nonlinearity