Abstract
In this paper we study the long-time behavior of a 2D Navier–Stokes equation. It is shown that under small forcing intensity the global attractor of the equation is a singleton. When endowed with additive or multiplicative white noise no sufficient evidence was found that the random attractor keeps the singleton structure, but the estimate of the convergence rate of the random attractor towards the deterministic singleton attractor as stochastic perturbation vanishes is obtained.
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Acknowledgements
H. Cui was partially funded by NSFC Grant 11801195 and the Fundamental Research Funds for the Central Universities 5003011026.
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Cui, H., Kloeden, P.E. (2021). Convergence Rate of Random Attractors for 2D Navier–Stokes Equation Towards the Deterministic Singleton Attractor. In: Sadovnichiy, V.A., Zgurovsky, M.Z. (eds) Contemporary Approaches and Methods in Fundamental Mathematics and Mechanics. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-030-50302-4_10
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