Communications in Mathematical Sciences

Volume 11 (2013)

Number 2

A remark on the box-counting dimension of the singular set for the Navier–Stokes equations

Pages: 597 – 602

DOI: http://dx.doi.org/10.4310/CMS.2013.v11.n2.a14

Author

Witold Sadowski (Faculty of Mathematics, Informatics and Mechanics, University of Warsaw, Poland)

Abstract

Let $u$ be a suitable weak solution of the Navier–Stokes equations and let $S$ be the set of its singular points in space-time. We prove that if $u_t$ is square integrable then the box-counting dimension of $S$ is no larger than one.

Keywords

Navier–Stokes equations, singular set, partial regularity, box-counting dimension

2010 Mathematics Subject Classification

35K55, 35Q30, 35Q35

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