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Regularity criterion for solutions to the Navier-Stokes equations in the whole 3D space based on two vorticity components
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SYSNO ASEP 0480807 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title Regularity criterion for solutions to the Navier-Stokes equations in the whole 3D space based on two vorticity components Author(s) Guo, Z. (CN)
Kučera, P. (CZ)
Skalák, Zdeněk (UH-J) SAI, ORCID, RIDSource Title Journal of Mathematical Analysis and Applications. - : Elsevier - ISSN 0022-247X
Roč. 458, č. 1 (2018), s. 755-766Number of pages 12 s. Publication form Print - P Language eng - English Country US - United States Keywords Navier Stokes equations ; conditional regularity ; regularity criteria ; vorticity ; Besov spaces ; bony decomposition Subject RIV BA - General Mathematics OECD category Fluids and plasma physics (including surface physics) R&D Projects GA13-00522S GA ČR - Czech Science Foundation (CSF) Institutional support UH-J - RVO:67985874 UT WOS 000413388800044 EID SCOPUS 85032152315 DOI 10.1016/j.jmaa.2017.09.029 Annotation We prove, among others, the following regularity criterion for the solutions to the Navier Stokes equations: If u is a global weak solution satisfying the energy inequality and omega = del x u, then u is regular on (0, T), T > 0, if two components of w belong to the space L-q (0, T, B-infinity infinity(-3/p)) for p is an element of (3, infinity) and 2/q + 3/p = 2. This result is an improvement of the results presented by Chae and Choe (1999) [7] or Zhang and Chen (2005) [38]. Our method of the proof uses a suitable application of the Bony decomposition and can also be used for the proofs of some other kin criteria. Otte such example is presented in Appendix. (C) 2017 Elsevier Inc. All rights reserved. Workplace Institute of Hydrodynamics Contact Soňa Hnilicová, hnilicova@ih.cas.cz, Tel.: 233 109 003 Year of Publishing 2019
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