Ergodic theory for energetically open compressible fluid flows

Fanelli F, Feireisl E, Hofmanová M (2021)
Physica D: Nonlinear Phenomena 423: 132914.

Zeitschriftenaufsatz | Veröffentlicht | Englisch
 
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Autor*in
Fanelli, Francesco; Feireisl, Eduard; Hofmanová, MartinaUniBi
Abstract / Bemerkung
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 is an element of R). In particular, the ergodic averages converge for any trajectory provided its omega-limit set in the trajectory space supports a unique (in law) stationary solution. (C) 2021 Elsevier B.V. All rights reserved.
Stichworte
Barotropic Navier-Stokes system; Ergodic theory; Inflow/outflow boundary; conditions; Stationary statistical solution
Erscheinungsjahr
2021
Zeitschriftentitel
Physica D: Nonlinear Phenomena
Band
423
Art.-Nr.
132914
ISSN
0167-2789
eISSN
1872-8022
Page URI
https://pub.uni-bielefeld.de/record/2956012

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Fanelli F, Feireisl E, Hofmanová M. Ergodic theory for energetically open compressible fluid flows. Physica D: Nonlinear Phenomena. 2021;423: 132914.
Fanelli, F., Feireisl, E., & Hofmanová, M. (2021). Ergodic theory for energetically open compressible fluid flows. Physica D: Nonlinear Phenomena, 423, 132914. https://doi.org/10.1016/j.physd.2021.132914
Fanelli, F., Feireisl, E., and Hofmanová, M. (2021). Ergodic theory for energetically open compressible fluid flows. Physica D: Nonlinear Phenomena 423:132914.
Fanelli, F., Feireisl, E., & Hofmanová, M., 2021. Ergodic theory for energetically open compressible fluid flows. Physica D: Nonlinear Phenomena, 423: 132914.
F. Fanelli, E. Feireisl, and M. Hofmanová, “Ergodic theory for energetically open compressible fluid flows”, Physica D: Nonlinear Phenomena, vol. 423, 2021, : 132914.
Fanelli, F., Feireisl, E., Hofmanová, M.: Ergodic theory for energetically open compressible fluid flows. Physica D: Nonlinear Phenomena. 423, : 132914 (2021).
Fanelli, Francesco, Feireisl, Eduard, and Hofmanová, Martina. “Ergodic theory for energetically open compressible fluid flows”. Physica D: Nonlinear Phenomena 423 (2021): 132914.

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