Random attractors for stochastic 2D-Navier-Stokes equations in some unbounded domains

Zdzislaw Brzezniak; T Caraballo; J.A. Langa; J. Real; G. Lukaszewicz; Y. Li

Random attractors for stochastic 2D-Navier-Stokes equations in some unbounded domains

Zdzislaw Brzezniak, T Caraballo, J.A. Langa, J. Real, G. Lukaszewicz, Y. Li

Mathematics

Research output: Working paper › Preprint

Abstract

We show that the stochastic flow generated by the Stochastic Navier-Stokes equations in a 2-dimensional Poincar\'e domain has a unique random attractor. This result complements a recent result by Brze\'zniak and Li \cite{Brz_Li_2006b} who showed that the flow is asymptotically compact and generalizes a recent result by Caraballo et al. \cite{Caraballo_L_R_2006} who proved existence of a unique pullback attractor for the time-dependent deterministic Navier-Stokes equations in a 2-dimensional Poincar\'e domain.

Original language	English
Number of pages	29
Publication status	Published - Mar 2011

Access to Document

http://arxiv.org/abs/1103.3889

Cite this

@techreport{3b7eef3321004976b6c6e7f3f79e0dc7,

title = "Random attractors for stochastic 2D-Navier-Stokes equations in some unbounded domains",

abstract = "We show that the stochastic flow generated by the Stochastic Navier-Stokes equations in a 2-dimensional Poincar\'e domain has a unique random attractor. This result complements a recent result by Brze\'zniak and Li \cite{Brz_Li_2006b} who showed that the flow is asymptotically compact and generalizes a recent result by Caraballo et al. \cite{Caraballo_L_R_2006} who proved existence of a unique pullback attractor for the time-dependent deterministic Navier-Stokes equations in a 2-dimensional Poincar\'e domain. ",

author = "Zdzislaw Brzezniak and T Caraballo and J.A. Langa and J. Real and G. Lukaszewicz and Y. Li",

year = "2011",

month = mar,

language = "English",

type = "WorkingPaper",

}

TY - UNPB

T1 - Random attractors for stochastic 2D-Navier-Stokes equations in some unbounded domains

AU - Brzezniak, Zdzislaw

AU - Caraballo, T

AU - Langa, J.A.

AU - Real, J.

AU - Lukaszewicz, G.

AU - Li, Y.

PY - 2011/3

Y1 - 2011/3

N2 - We show that the stochastic flow generated by the Stochastic Navier-Stokes equations in a 2-dimensional Poincar\'e domain has a unique random attractor. This result complements a recent result by Brze\'zniak and Li \cite{Brz_Li_2006b} who showed that the flow is asymptotically compact and generalizes a recent result by Caraballo et al. \cite{Caraballo_L_R_2006} who proved existence of a unique pullback attractor for the time-dependent deterministic Navier-Stokes equations in a 2-dimensional Poincar\'e domain.

AB - We show that the stochastic flow generated by the Stochastic Navier-Stokes equations in a 2-dimensional Poincar\'e domain has a unique random attractor. This result complements a recent result by Brze\'zniak and Li \cite{Brz_Li_2006b} who showed that the flow is asymptotically compact and generalizes a recent result by Caraballo et al. \cite{Caraballo_L_R_2006} who proved existence of a unique pullback attractor for the time-dependent deterministic Navier-Stokes equations in a 2-dimensional Poincar\'e domain.

M3 - Preprint

BT - Random attractors for stochastic 2D-Navier-Stokes equations in some unbounded domains

ER -