Electron. J. Diff. Equ., Vol. 2012 (2012), No. 59, pp. 1-18.

Periodic random attractors for stochastic Navier-Stokes equations on unbounded domains

Bixiang Wang

This article concerns the asymptotic behavior of solutions to the two-dimensional Navier-Stokes equations with both non-autonomous deterministic and stochastic terms defined on unbounded domains. First we introduce a continuous cocycle for the equations and then prove the existence and uniqueness of tempered random attractors. We also characterize the structures of the random attractors by complete solutions. When deterministic forcing terms are periodic, we show that the tempered random attractors are also periodic. Since the Sobolev embeddings on unbounded domains are not compact, we establish the pullback asymptotic compactness of solutions by Ball's idea of energy equations.

Submitted February 13, 2012. Published April 12, 2012.
Math Subject Classifications: 35B40, 35B41, 37L30.
Key Words: Random attractor; stochastic Navier-Stokes equation; unbounded domain; complete solution.

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Bixiang Wang
Department of Mathematics
New Mexico Institute of Mining and Technology
Socorro, NM 87801, USA
email: bwang@nmt.edu

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