Ergodic theory for energetically open compressible fluid flows

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F21%3A00542582" target="_blank" >RIV/67985840:_____/21:00542582 - isvavai.cz</a>

Výsledek na webu

<a href="https://doi.org/10.1016/j.physd.2021.132914" target="_blank" >https://doi.org/10.1016/j.physd.2021.132914</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.physd.2021.132914" target="_blank" >10.1016/j.physd.2021.132914</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Ergodic theory for energetically open compressible fluid flows

Popis výsledku v původním jazyce

The ergodic hypothesis is examined for energetically open fluid systems represented by the barotropic Navier–Stokes equations with general inflow/outflow boundary conditions. We show that any globally bounded trajectory generates a stationary statistical solution, which is interpreted as a stochastic process with continuous trajectories supported by the family of weak solutions of the problem. The abstract Birkhoff–Khinchin theorem is applied to obtain convergence (in expectation and a.s.) of ergodic averages for any bounded Borel measurable function of state variables associated to any stationary solution. Finally, we show that validity of the ergodic hypothesis is determined by the behavior of entire solutions (i.e. a solution defined for any t∈R). In particular, the ergodic averages converge for any trajectory provided its ω-limit set in the trajectory space supports a unique (in law) stationary solution.

Název v anglickém jazyce

Ergodic theory for energetically open compressible fluid flows

Popis výsledku anglicky

The ergodic hypothesis is examined for energetically open fluid systems represented by the barotropic Navier–Stokes equations with general inflow/outflow boundary conditions. We show that any globally bounded trajectory generates a stationary statistical solution, which is interpreted as a stochastic process with continuous trajectories supported by the family of weak solutions of the problem. The abstract Birkhoff–Khinchin theorem is applied to obtain convergence (in expectation and a.s.) of ergodic averages for any bounded Borel measurable function of state variables associated to any stationary solution. Finally, we show that validity of the ergodic hypothesis is determined by the behavior of entire solutions (i.e. a solution defined for any t∈R). In particular, the ergodic averages converge for any trajectory provided its ω-limit set in the trajectory space supports a unique (in law) stationary solution.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/GA18-05974S" target="_blank" >GA18-05974S: Oscilace a koncentrace proti stabilitě v rovnicích pohybu tekutin</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Physica. D

ISSN

0167-2789

e-ISSN

1872-8022

Svazek periodika

423

Číslo periodika v rámci svazku

September

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

25

Strana od-do

132914

Kód UT WoS článku

000661734700006

EID výsledku v databázi Scopus

2-s2.0-85105699010