A note on the regularity of the solutions to the Navier-Stokes equations via the gradient of one velocity component

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F14%3A00227615" target="_blank" >RIV/68407700:21110/14:00227615 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1063/1.4904836" target="_blank" >http://dx.doi.org/10.1063/1.4904836</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1063/1.4904836" target="_blank" >10.1063/1.4904836</a>

Result language
angličtina
Original language name
A note on the regularity of the solutions to the Navier-Stokes equations via the gradient of one velocity component
Original language description
We present a regularity criterion for the solutions to the Navier-Stokes equations based on the gradient of one velocity component. Starting with the method developed in cite{CaTi} for the case of one entry of the velocity gradient and using further someinequalities concerning the anisotropic Sobolev spaces, we show as a main result that a weak solution $u$ is regular on $(0,T)$, $T>0$, provided that $nabla u_3 in L^t(0,T;L^s)$, where $2/t+3/s = 3/2+3/(4s)$ and $s in (3/2,2)$. It improves the known results for $s in (3/2,15/8)$.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2014
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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