Regularity criterion for solutions to the Navier-Stokes equations in the whole 3D space based on two vorticity components
Result description
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.
Keywords
Navier Stokes equationsconditional regularityregularity criteriavorticityBesov spacesbony decomposition
The result's identifiers
Result code in IS VaVaI
Alternative codes found
RIV/68407700:21110/18:00321862
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Regularity criterion for solutions to the Navier-Stokes equations in the whole 3D space based on two vorticity components
Original language description
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.
Czech name
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Czech description
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Classification
Type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10305 - Fluids and plasma physics (including surface physics)
Result continuities
Project
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Mathematical Analysis and Applications
ISSN
0022-247X
e-ISSN
—
Volume of the periodical
458
Issue of the periodical within the volume
1
Country of publishing house
US - UNITED STATES
Number of pages
12
Pages from-to
755-766
UT code for WoS article
000413388800044
EID of the result in the Scopus database
2-s2.0-85032152315
Basic information
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Fluids and plasma physics (including surface physics)
Year of implementation
2018