Electron. J. Diff. Equ.,
Vol. 2012 (2012), No. 59, pp. 118.
Periodic random attractors for stochastic NavierStokes equations
on unbounded domains
Bixiang Wang
Abstract:
This article concerns the asymptotic behavior of solutions
to the twodimensional NavierStokes equations with both
nonautonomous 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 NavierStokes 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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