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Article

Homogenization of trajectory attractors of 3D Navier-Stokes system with randomly oscillating force

Discrete and Continuous Dynamical Systems. 2017. Vol. 37. No. 5. P. 2375-2393.
Bekmaganbetov K. A., Chechkin G. A., Chepyzhov V. V., Goritsky A. Y.

We consider the 3D Navier--Stokes systems with randomly rapidly oscillating right--hand sides. Under the assumption that the random functions are ergodic and statistically homogeneous in space variables or in time variables we prove that the trajectory attractors of these systems tend to the trajectory attractors of homogenized 3D Navier--Stokes systems whose right--hand sides are the average of the corresponding terms of the original systems. We do not assume that the Cauchy problem for the considered 3D Navier--Stokes systems is uniquely solvable.