The large-time energy concentration in solutions to the Navier-Stokes equations with nonzero external forces

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985874%3A_____%2F13%3A00395206" target="_blank" >RIV/67985874:_____/13:00395206 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.jmaa.2013.01.010" target="_blank" >http://dx.doi.org/10.1016/j.jmaa.2013.01.010</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.jmaa.2013.01.010" target="_blank" >10.1016/j.jmaa.2013.01.010</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The large-time energy concentration in solutions to the Navier-Stokes equations with nonzero external forces

Popis výsledku v původním jazyce

It is known that the turbulent solutions to the unforced Navier-Stokes equations exhibit a large-time energy concentration in the frequency space. If we suppose the existence of a nonzero time dependent external force f is an element of L-1((0, infinity); L-sigma(2)) in the equations, the situation is more complicated. It is possible to construct simple examples of solutions, in which the energy is asymptotically distributed over the entire spectrum of the Stokes operator. Further, we will show as the main result of this paper that there still exist wide classes of initial conditions and external forces yielding solutions with the large-time energy concentration analogical to the situation in the unforced Navier-Stokes equations. We will also show thatthe frequency spectrum of the solution does not generally relate to the frequency spectrum of the external force.

Název v anglickém jazyce

The large-time energy concentration in solutions to the Navier-Stokes equations with nonzero external forces

Popis výsledku anglicky

It is known that the turbulent solutions to the unforced Navier-Stokes equations exhibit a large-time energy concentration in the frequency space. If we suppose the existence of a nonzero time dependent external force f is an element of L-1((0, infinity); L-sigma(2)) in the equations, the situation is more complicated. It is possible to construct simple examples of solutions, in which the energy is asymptotically distributed over the entire spectrum of the Stokes operator. Further, we will show as the main result of this paper that there still exist wide classes of initial conditions and external forces yielding solutions with the large-time energy concentration analogical to the situation in the unforced Navier-Stokes equations. We will also show thatthe frequency spectrum of the solution does not generally relate to the frequency spectrum of the external force.

Druh

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

CEP obor

BK - Mechanika tekutin

OECD FORD obor

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Projekt

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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 Applications

ISSN

0022-247X

e-ISSN

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Svazek periodika

402

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

10

Strana od-do

147-156

Kód UT WoS článku

000315836900013

EID výsledku v databázi Scopus

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