Ergodic theory for energetically open compressible fluid flows
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
Ergodic theory for energetically open compressible fluid flows
Original language description
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.
Czech name
—
Czech description
—
Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics
Result continuities
Project
<a href="/en/project/GA18-05974S" target="_blank" >GA18-05974S: Oscillations and concentrations versus stability in the equations of mathematical fluid dynamics</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Physica. D
ISSN
0167-2789
e-ISSN
1872-8022
Volume of the periodical
423
Issue of the periodical within the volume
September
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
25
Pages from-to
132914
UT code for WoS article
000661734700006
EID of the result in the Scopus database
2-s2.0-85105699010