The large-time energy concentration in solutions to the Navier-Stokes equations in the frequency space

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

The large-time energy concentration in solutions to the Navier-Stokes equations in the frequency space

Popis výsledku v původním jazyce

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

Název v anglickém jazyce

The large-time energy concentration in solutions to the Navier-Stokes equations in the frequency space

Popis výsledku anglicky

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

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2013

Kód důvěrnosti údajů

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

Název periodika

Journal of Mathematical Analysis and Its Applications

ISSN

0022-247X

e-ISSN

—

Svazek periodika

400

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

21

Strana od-do

689-709

Kód UT WoS článku

000314075600034

EID výsledku v databázi Scopus

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