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Funktsional. Anal. i Prilozhen., 2004, Volume 38, Issue 1, Pages 34–46 (Mi faa94)  

This article is cited in 11 scientific papers (total in 11 papers)

On Random Attractors for Mixing Type Systems

S. B. Kuksinab, A. R. Shirikyana

a Heriot Watt University
b Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: The paper deals with infinite-dimensional random dynamical systems. Under the condition that the system in question is of mixing type and possesses a random compact attracting set, we show that the support of the unique invariant measure is the minimal random point attractor. The results obtained apply to the randomly forced 2D Navier–Stokes system.

Keywords: invariant measure, mixing type system, random attractor, stationary measure, 2D Navier–Stokes equations


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English version:
Functional Analysis and Its Applications, 2004, 38:1, 28–37

Bibliographic databases:

UDC: 517.95+517.946
Received: 02.09.2002

Citation: S. B. Kuksin, A. R. Shirikyan, “On Random Attractors for Mixing Type Systems”, Funktsional. Anal. i Prilozhen., 38:1 (2004), 34–46; Funct. Anal. Appl., 38:1 (2004), 28–37

Citation in format AMSBIB
\by S.~B.~Kuksin, A.~R.~Shirikyan
\paper On Random Attractors for Mixing Type Systems
\jour Funktsional. Anal. i Prilozhen.
\yr 2004
\vol 38
\issue 1
\pages 34--46
\jour Funct. Anal. Appl.
\yr 2004
\vol 38
\issue 1
\pages 28--37

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    This publication is cited in the following articles:
    1. Zhou Shengfan, Yin Fuqi, Ouyang Zigen, “Random attractor for damped nonlinear wave equations with white noise”, SIAM J. Appl. Dyn. Syst., 4:4 (2005), 883–903  crossref  mathscinet  zmath  isi  elib  scopus
    2. Ghil M., Chekroun M.D., Simonnet E., “Climate dynamics and fluid mechanics: Natural variability and related uncertainties”, Phys. D, 237:14-17 (2008), 2111–2126  crossref  mathscinet  zmath  isi  elib  scopus
    3. Scheutzow M., “Attractors for ergodic and monotone random dynamical systems”, Seminar on Stochastic Analysis, Random Fields and Applications V, Progress in Probability, 59, 2008, 331–344  crossref  mathscinet  zmath  isi
    4. van Bargen H., Dimitroff G., “Isotropic Ornstein–Uhlenbeck flows”, Stochastic Processes Appl., 119:7 (2009), 2166–2197  crossref  mathscinet  zmath  isi  scopus
    5. Beyn W.-J., Gess B., Lescot P., Roeckner M., “The Global Random Attractor for a Class of Stochastic Porous Media Equations”, Comm Partial Differential Equations, 36:3 (2011), 446–469  crossref  mathscinet  zmath  isi  scopus
    6. Gess B., Liu W., Roeckner M., “Random attractors for a class of stochastic partial differential equations driven by general additive noise”, J Differential Equations, 251:4–5 (2011), 1225–1253  crossref  mathscinet  zmath  adsnasa  isi  scopus
    7. Gess B., “Random Attractors for Degenerate Stochastic Partial Differential Equations”, J. Dyn. Differ. Equ., 25:1 (2013), 121–157  crossref  mathscinet  zmath  isi  scopus
    8. Guzik G., “Asymptotic Properties of Multifunctions, Families of Measures and Markov Operators Associated With Cocycles”, Nonlinear Anal.-Theory Methods Appl., 130 (2016), 59–75  crossref  mathscinet  zmath  isi  scopus
    9. Ghil M., “The wind-driven ocean circulation: Applying dynamical systems theory to a climate problem”, Discret. Contin. Dyn. Syst., 37:1 (2017), 189–228  crossref  mathscinet  zmath  isi  elib  scopus
    10. Kuksin S., Shirikyan A., “Rigorous Results in Space-Periodic Two-Dimensional Turbulence”, Phys. Fluids, 29:12 (2017), 125106  crossref  isi  scopus
    11. Dong Zh., Zhang R., “Long-Time Behavior of 3D Stochastic Planetary Geostrophic Viscous Model”, Stoch. Dyn., 18:5 (2018), 1850038  crossref  mathscinet  zmath  isi  scopus
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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