Regularity criteria of the incompressible Navier-Stokes equations via only one entry of velocity gradient

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985874%3A_____%2F19%3A00505896" target="_blank" >RIV/67985874:_____/19:00505896 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1007%2Fs00021-019-0441-6" target="_blank" >https://link.springer.com/article/10.1007%2Fs00021-019-0441-6</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s00021-019-0441-6" target="_blank" >10.1007/s00021-019-0441-6</a>

Result language
angličtina
Original language name
Regularity criteria of the incompressible Navier-Stokes equations via only one entry of velocity gradient
Original language description
In this paper we establish regularity conditions for the three dimensional incompressible Navier-Stokes equationsin terms of one entry of the velocity gradient tensor, say for example,∂3u3. We show that if∂3u3satisfies certain integrableconditions with respect to time and space variables in anisotropic Lebesgue spaces, then a Leray-Hopf weak solution isactually regular. The anisotropic Lebesgue space helps us to almost reach the Prodi-Serrin level 2 in certain special case.Moreover, regularity conditions on non-diagonal element of gradient tensor∂1u3are also established, which covers someprevious 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
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OECD FORD branch
10305 - Fluids and plasma physics (including surface physics)

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
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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