An optimal regularity criterion for the Navier–Stokes equations proved by a blow-up argument
Result description
We study the conditional regularity for the incompressible Navier–Stokes equations in terms of one directional derivative of the velocity field. We show that if u is a weak solution in the whole three dimensional space and ∂3u∈Lp(0,T,Lq(R3)), T>0, where 2∕p+3∕q=2 and q∈(3,19∕6], then u is regular on (0,T], crossing so for the first time the barrier q=3. The proof is based on a suitable combination of a blow-up argument and mutual estimates of certain integral quantities pertained to the rescaled solution.
Keywords
conditional regularityNavier-Stokes equationsregularity criteriarescaling procedure
The result's identifiers
Result code in IS VaVaI
Result on the web
https://www.sciencedirect.com/science/article/pii/S1468121820301255
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
An optimal regularity criterion for the Navier–Stokes equations proved by a blow-up argument
Original language description
We study the conditional regularity for the incompressible Navier–Stokes equations in terms of one directional derivative of the velocity field. We show that if u is a weak solution in the whole three dimensional space and ∂3u∈Lp(0,T,Lq(R3)), T>0, where 2∕p+3∕q=2 and q∈(3,19∕6], then u is regular on (0,T], crossing so for the first time the barrier q=3. The proof is based on a suitable combination of a blow-up argument and mutual estimates of certain integral quantities pertained to the rescaled solution.
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
10102 - Applied mathematics
Result continuities
Project
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Nonlinear Analysis: Real World Applications
ISSN
1468-1218
e-ISSN
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Volume of the periodical
58
Issue of the periodical within the volume
April
Country of publishing house
GB - UNITED KINGDOM
Number of pages
7
Pages from-to
103207
UT code for WoS article
000595257700015
EID of the result in the Scopus database
2-s2.0-85090051738
Basic information
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Applied mathematics
Year of implementation
2021