A note on lower bounds of decay rates for solutions to the Navier-Stokes equations in the norms of Besov spaces

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F14%3A00227614" target="_blank" >RIV/68407700:21110/14:00227614 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.na.2013.11.007" target="_blank" >http://dx.doi.org/10.1016/j.na.2013.11.007</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.na.2013.11.007" target="_blank" >10.1016/j.na.2013.11.007</a>

Result language
angličtina
Original language name
A note on lower bounds of decay rates for solutions to the Navier-Stokes equations in the norms of Besov spaces
Original language description
We study the lower bounds of decay rates for turbulent solutions to the Navier-Stokes equations in the norms of Besov spaces. We focus on solutions satisfying $0 < liminf_{t rightarrow infty} t^gamma ||u(t)|| le limsup_{t rightarrow infty} t^gamma ||u(t)|| < infty$ for some $gamma in (0,5/4]$ and prove among others that such solutions, measured in the norm of the Besov space $dot{B}^{-2gamma}_{2,infty}$, are estimated for large times from below by some positive constant. These estimates stem from sufficiently fast rate of large time energy concentration in low frequencies occurring in the studied solutions. Our results have simple proofs and improve and extend substantially the results published by Miyakawa in cite{Mi} and by Schonbek and Wiegner in cite{SchWi}
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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