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%3A00227613" target="_blank" >RIV/68407700:21110/14:00227613 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.na.2014.03.018" target="_blank" >http://dx.doi.org/10.1016/j.na.2014.03.018</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.na.2014.03.018" target="_blank" >10.1016/j.na.2014.03.018</a>

Result language
angličtina
Original language name
On the regularity of the solutions to the Navier-Stokes equations via the gradient of one velocity component
Original language description
We improve a regularity criterion for the solutions to the Navier-Stokes equations in the full three-dimensional space involving the gradient of one velocity component. Revising the method used in cite{PoZh} and cite{PoZh2}, we show that a weak solution$u$ is regular on $(0,T)$ provided that $nabla u_3 in L^t(0,T;L^s)$, where $2/t+3/s = 19/10$ for $s in [30/19,10/3]$ and $2/t+3/s = 7/4+1/(2s)$ for $s in [10/3,infty]$. It improves the known results for $s in [30/19,150/77)$ and $s in (10/3,infty]$
Czech name
—
Czech description
—

Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
—

Project
—
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

Similar results(10)