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Ergodic theory for energetically open compressible fluid flows
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SYSNO ASEP 0542582 Druh ASEP J - Článek v odborném periodiku Zařazení RIV J - Článek v odborném periodiku Poddruh J Článek ve WOS Název Ergodic theory for energetically open compressible fluid flows Tvůrce(i) Fanelli, F. (FR)
Feireisl, Eduard (MU-W) RID, SAI, ORCID
Hofmanová, M. (DE)Číslo článku 132914 Zdroj.dok. Physica. D. - : Elsevier - ISSN 0167-2789
Roč. 423, September (2021)Poč.str. 25 s. Jazyk dok. eng - angličtina Země vyd. NL - Nizozemsko Klíč. slova barotropic Navier-Stokes system ; ergodic theory ; inflow/outflow boundary conditions ; stationary statistical solution Vědní obor RIV BA - Obecná matematika Obor OECD Pure mathematics CEP GA18-05974S GA ČR - Grantová agentura ČR Způsob publikování Omezený přístup Institucionální podpora MU-W - RVO:67985840 UT WOS 000661734700006 EID SCOPUS 85105699010 DOI 10.1016/j.physd.2021.132914 Anotace 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. Pracoviště Matematický ústav Kontakt Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Rok sběru 2022 Elektronická adresa https://doi.org/10.1016/j.physd.2021.132914
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