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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.

MSC:
37A99Ergodic theory
37C70Attractors and repellers, topological structure
35K57Reaction-diffusion equations
35Q30Stokes and Navier-Stokes equations
60H15Stochastic partial differential equations
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