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Remarks on regularity criteria for the Navier-Stokes equations via one velocity component
Journal article   Peer reviewed

Remarks on regularity criteria for the Navier-Stokes equations via one velocity component

Xuanji Jia and Yong Zhou
Nonlinear analysis: real world applications, Vol.15(1), pp.239-245
01/01/2014
DOI: https://doi.org/10.1016/j.nonrwa.2013.08.002

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
Recently, Pokorny and Zhou proved that if parallel to u(3)parallel to(L infinity (0,T;L) (10/3) ((R3))) << 1 or parallel to del u(3)parallel to(L infinity(0,T;L) (30/19) ((R3))) << 1, then the weak solution u of the 3D Navier-Stokes equations is regular on R-3 x (0, T]. In this paper we remove the smallness assumptions by using a new approach which may be of independent interest and further application. (C) 2013 Elsevier Ltd. All rights reserved.

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