An optimal regularity criterion for the Navier–Stokes equations proved by a blow-up argument

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985874%3A_____%2F21%3A00532070" target="_blank" >RIV/67985874:_____/21:00532070 - isvavai.cz</a>
Result on the web
<a href="https://www.sciencedirect.com/science/article/pii/S1468121820301255" target="_blank" >https://www.sciencedirect.com/science/article/pii/S1468121820301255</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.nonrwa.2020.103207" target="_blank" >10.1016/j.nonrwa.2020.103207</a>

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
—
Czech description
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Type
J<sub>imp</sub> - 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

Project
<a href="/en/project/GA18-09628S" target="_blank" >GA18-09628S: Advanced flow-field analysis</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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