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Licensed Unlicensed Requires Authentication Published by Oldenbourg Wissenschaftsverlag August 27, 2015

A regularity criterion of Serrin-type for the Navier–Stokes equations involving the gradient of one velocity component

  • Jörg Wolf EMAIL logo
From the journal Analysis


In the present paper we prove that a weak Leray solution to the Navier–Stokes equations in 3×(0,T] is regular provided the gradient of one component belongs to the Prodi–Serrin class u3L4(0,T;L2).

Funding source: Korea Federation of Science and Technology Societies

Award Identifier / Grant number: Brain Pool Project 141S-1-3-0022

The author wishes to thank the organizers of the Luminy conference for the opportunity to present his result. Additionally, thanks to Prof. Y. Zhou for his invitation to the first joint Chinese-German conference on fluid and gas dynamics in Jinhua, China 2010, where parts of the result (in particular the method illustrated in the appendix) were presented.

Received: 2014-12-3
Revised: 2015-5-14
Accepted: 2015-8-6
Published Online: 2015-8-27
Published in Print: 2015-11-1

© 2015 by De Gruyter

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