The interior regularity of pressure associated with a weak solution to the Navier-Stokes equations with the Navier-type boundary conditions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F18%3A00489052" target="_blank" >RIV/67985840:_____/18:00489052 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jmaa.2018.03.017" target="_blank" >http://dx.doi.org/10.1016/j.jmaa.2018.03.017</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2018.03.017" target="_blank" >10.1016/j.jmaa.2018.03.017</a>

Result language
angličtina
Original language name
The interior regularity of pressure associated with a weak solution to the Navier-Stokes equations with the Navier-type boundary conditions
Original language description
We prove that if u is a weak solution to the Navier-Stokes system with the Navier-type boundary conditions in Omega x (0,T), satisfying the strong energy inequality in Omega x (0,T) and Serrin's integrability conditions in Omega' x (t1,t2) (where Omega' is a sub-domain of Omega and 0<= t1<t2<=T) then p and the time-derivative of u have spatial derivatives of all orders essentially bounded in Omega'' x (t1+e,t2-e) for any bounded sub-domain Omega'' of Omega' and e>0 so small that t1+e<t2-e. (See Theorem 1.) We show an application of Theorem 1 to the procedure of localization.
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
10101 - Pure mathematics

Project
<a href="/en/project/GA17-01747S" target="_blank" >GA17-01747S: Theory and numerical analysis of coupled problems in fluid dynamics</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2018
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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