A regularity criterion for the Navier-Stokes equations via one diagonal entry of the velocity gradient

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F21%3A00365435" target="_blank" >RIV/68407700:21110/21:00365435 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.4310/CMS.2021.v19.n4.a10" target="_blank" >https://doi.org/10.4310/CMS.2021.v19.n4.a10</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4310/CMS.2021.v19.n4.a10" target="_blank" >10.4310/CMS.2021.v19.n4.a10</a>

Result language
angličtina
Original language name
A regularity criterion for the Navier-Stokes equations via one diagonal entry of the velocity gradient
Original language description
We study the conditional regularity of solutions to the Navier-Stokes equations in the three dimensional space. Let u=(u(1),u(2),u(3)) denote the velocity. We impose an additional condition only on one diagonal entry of the velocity gradient, namely partial derivative(3)u(3), and show, using a technique based on the mixed multiplier theorem and an anisotropic version of the Troisi inequality, that if partial derivative(3)u(3) lies in the space L-beta(0,T;L-q) with suitable beta,q, then u is regular on (0,T]. Our result improves and extends the analogous results known from the literature.
Czech name
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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
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Center for advanced applied science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

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

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