Random attractors. (English) Zbl 0884.58064

Every scientist interested in the behavior of dynamical systems knows that this is one of the most important subjects of mathematical physics. It is also well-known that good results can be obtained by studying the global attractor of such a deterministic dynamical system.
Even though there are a lot of papers devoted to this subject, the authors successfully succeed to offer an accurate and clear treatment of this problem. Their paper contains several graduated sections. The first of them, after an introduction, presents the authors’ notion of an attractor in the case of a nonautonomous deterministic system. Based on this notion, the authors introduce the preliminary assumptions regarding stochastic dynamical systems and they develop the main result of the paper in the second part. The last of the sections is devoted to three applications: the Navier-Stokes equations perturbed by an additive noise, the white noise-driven Burgers equation and the random attractor for a nonlinear random wave equation.
Reviewer: I.Grosu (Iaşi)


37C70 Attractors and repellers of smooth dynamical systems and their topological structure
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