The relationship between random attractors and global attractors for dynamical systems is studied. If a partial differential equation is perturbed by an E-small random term and certain hypotheses are satisfied, the upper semicontinuity of the random attractors is obtalned as c goes to zero. The results are applied to the Navier-Stokes equations and a problem of reaction-diffusion type, both perturbed by an additive white noise.
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Caraballo et al. (1998) studied this question.
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