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Attractors for random dynamical systems. (English) Zbl 0819.58023
Random dynamical systems are treated, the notions of an omega limit set, a random invariant set, an absorbing set and a global attractor are introduced. Conditions are given under which a global attractor (being a compact random invariant set) exists, and some of its properties are established. The theory is then applied to a reaction-diffusion equation with additive noise and to the stochastic Navier-Stokes equation with multiplicative, resp. additive noise. In all the three cases the existence of a compact stochastic attractor is proved.

37A99 Ergodic theory
37C70 Attractors and repellers of smooth dynamical systems and their topological structure
35K57 Reaction-diffusion equations
35Q30 Navier-Stokes equations
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
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