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May  2018, 23(3): 1297-1324. doi: 10.3934/dcdsb.2018152

## Squeezing and finite dimensionality of cocycle attractors for 2D stochastic Navier-Stokes equation with non-autonomous forcing

 1 School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China 2 Departamento de Matemática, Universidade Federal do Pará, Rua Augusto Corrêa s/n, 66000-000, Belém PA, Brazil 3 Departamento de Ecuaciones Diferenciales Análisis Numérico, Universidad de Sevilla, Apdo. de Correos 1160, 41080-Sevilla, Spain

Dedicated to the memory of professor Igor Chueshov

Received  May 2017 Revised  September 2017 Published  May 2018 Early access  February 2018

In this paper, we study the squeezing property and finite dimensionality of cocycle attractors for non-autonomous dynamical systems (NRDS). We show that the generalized random cocycle squeezing property (RCSP) is a sufficient condition to prove a determining modes result and the finite dimensionality of invariant non-autonomous random sets, where the upper bound of the dimension is uniform for all components of the invariant set. We also prove that the RCSP can imply the pullback flattening property in uniformly convex Banach space so that could also contribute to establish the asymptotic compactness of the system. The cocycle attractor for 2D Navier-Stokes equation with additive white noise and translation bounded non-autonomous forcing is studied as an application.

Citation: Hongyong Cui, Mirelson M. Freitas, José A. Langa. Squeezing and finite dimensionality of cocycle attractors for 2D stochastic Navier-Stokes equation with non-autonomous forcing. Discrete & Continuous Dynamical Systems - B, 2018, 23 (3) : 1297-1324. doi: 10.3934/dcdsb.2018152
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