Zhang, Qiangheng; Li, Yangrong Asymptotic autonomy of bi-spatial attractors for stochastic retarded Navier-Stokes equations. (English) Zbl 1483.35044 Topol. Methods Nonlinear Anal. 58, No. 2, 521-547 (2021). Summary: We establish semi-convergence of a non-autonomous bi-spatial random attractor towards to an autonomous attractor under the topology of the regular space when time-parameter goes to infinity, where the criteria are given by forward compactness of the attractor in the terminal space as well as forward convergence of the random dynamical system in the initial space. We then apply to both non-autonomous and autonomous stochastic 2D Navier-Stokes equations with general delays (including variable and distribution delays). The forward-pullback asymptotic compactness in the space of continuous Sobolev-valued functions is proved by the method of spectrum decomposition. Cited in 3 Documents MSC: 35B41 Attractors 35Q30 Navier-Stokes equations 37L55 Infinite-dimensional random dynamical systems; stochastic equations 60H15 Stochastic partial differential equations (aspects of stochastic analysis) Keywords:delay Navier-Stokes equations; bi-spatial random attractor; pullback attractor; asymptotic autonomy; forward controller × Cite Format Result Cite Review PDF Full Text: DOI References: [1] H. Bessaih and M.J. Garrido-Atienza, Longtime behavior for 3D Navier-Stokes equations with constant delays, Commun. Pure Appl. Anal. 19 (2020), 1931-1948. · Zbl 1437.35527 [2] H. Bessaih, M.J. Garrido-Atienza and B. Schmalfuss, On 3D Navier-Stokes equations: Regularization and uniqueness by delays, Physica D 376 (2018), 228-237. · Zbl 1398.76031 [3] Z. Brzezniak, T. Caraballo, J.A. Langa, Y.H. Li, G. Lukaszewicz and J. Real, Random attractors for stochastic 2D-Navier-Stokes equations in some unbounded domains, J. 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