The large-time energy concentration in solutions to the Navier-Stokes equations in the frequency space
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21110%2F13%3A00204172" target="_blank" >RIV/68407700:21110/13:00204172 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1016/j.jmaa.2012.11.004" target="_blank" >http://dx.doi.org/10.1016/j.jmaa.2012.11.004</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.jmaa.2012.11.004" target="_blank" >10.1016/j.jmaa.2012.11.004</a>
Alternative languages
Result language
angličtina
Original language name
The large-time energy concentration in solutions to the Navier-Stokes equations in the frequency space
Original language description
In the paper we study the large-time behavior of solutions to the Navier-Stokes equations in the frequency space. We describe in detail the large-time energy concentration which occurs in every (turbulent) solution. If the energy of the solution decreases exponentially then it concentrates in frequencies localized in an annulus in the frequency space. The annulus can be taken arbitrarily narrow and its diameter determines the rate of the exponential decay. All the other solutions are characterized by the concentration of the energy in the frequencies localized in a ball with an arbitrarily small diameter centered in the origin of the coordinates. It will follow from the presented results that the frequencies outside the annulus or the ball and especially the higher frequencies die out very quickly. We will further observe the concentration occurring in any time derivative of the solution or in the vorticity and its time derivatives with the same annulus or the ball for the particular s
Czech name
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Czech description
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Classification
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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Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Journal of Mathematical Analysis and Its Applications
ISSN
0022-247X
e-ISSN
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Volume of the periodical
400
Issue of the periodical within the volume
2
Country of publishing house
US - UNITED STATES
Number of pages
21
Pages from-to
689-709
UT code for WoS article
000314075600034
EID of the result in the Scopus database
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