Upper semicontinuity of attractors for small random perturbations of dynamical systems.

*(English)*Zbl 0917.35169The authors study the relationship between a random attractor and the deterministic one, when they apply to the deterministic partial differential equation a small random perturbation, whose strength is measured by a small parameter $\epsilon $.

Under some conditions, they prove that the random attractor is a perturbation of the deterministic one, in the sense that the upper-semicontinuity for random attractors is obtained as $\epsilon $ goes to zero. The results are applied to Navier-Stokes equations and to a problem of reaction-diffusion type, both perturbed by an additive white noise.

Reviewer: S.Méléard (Paris)