The Rayleigh-Bénard problem for compressible fluid flows

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F23%3A00567885" target="_blank" >RIV/67985840:_____/23:00567885 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1007/s00205-022-01837-6" target="_blank" >https://doi.org/10.1007/s00205-022-01837-6</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1007/s00205-022-01837-6" target="_blank" >10.1007/s00205-022-01837-6</a>

Jazyk výsledku

angličtina

Název v původním jazyce

The Rayleigh-Bénard problem for compressible fluid flows

Popis výsledku v původním jazyce

We consider the physically relevant fully compressible setting of the Rayleigh-Bénard problem of a fluid confined between two parallel plates, heated from the bottom, and subjected to gravitational force. Under suitable restrictions imposed on the constitutive relations we show that this open system is dissipative in the sense of Levinson, meaning there exists a bounded absorbing set for any global-in-time weak solution. In addition, global-in-time trajectories are asymptotically compact in suitable topologies and the system possesses a global compact trajectory attractor A. The standard technique of Krylov and Bogolyubov then yields the existence of an invariant measure - a stationary statistical solution sitting on A. In addition, the Birkhoff-Khinchin ergodic theorem provides convergence of ergodic averages of solutions belonging to A a.s. with respect to the invariant measure.

Název v anglickém jazyce

The Rayleigh-Bénard problem for compressible fluid flows

Popis výsledku anglicky

We consider the physically relevant fully compressible setting of the Rayleigh-Bénard problem of a fluid confined between two parallel plates, heated from the bottom, and subjected to gravitational force. Under suitable restrictions imposed on the constitutive relations we show that this open system is dissipative in the sense of Levinson, meaning there exists a bounded absorbing set for any global-in-time weak solution. In addition, global-in-time trajectories are asymptotically compact in suitable topologies and the system possesses a global compact trajectory attractor A. The standard technique of Krylov and Bogolyubov then yields the existence of an invariant measure - a stationary statistical solution sitting on A. In addition, the Birkhoff-Khinchin ergodic theorem provides convergence of ergodic averages of solutions belonging to A a.s. with respect to the invariant measure.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA21-02411S" target="_blank" >GA21-02411S: Řešení nekorektních úloh pohybu stlačitelných tekutin</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Archive for Rational Mechanics and Analysis

ISSN

0003-9527

e-ISSN

1432-0673

Svazek periodika

247

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

DE - Spolková republika Německo

Počet stran výsledku

31

Strana od-do

9

Kód UT WoS článku

000917250800001

EID výsledku v databázi Scopus

2-s2.0-85146628525