On exponential convergence to a stationary measure for a class of random dynamical systems. (English) Zbl 1213.37084

Kuksin, Sergei B.

Journées “Équations aux dérivées partielles”, Plestin-les-Grèves, France, 5 au 8 juin 2001. Exposés Nos. I-XIV. Nantes: Université de Nantes (ISBN 2-86939-169-2/pbk). Exp. No. 9, 10 p. (2001).

Summary: For a class of random dynamical systems which describe dissipative nonlinear PDEs perturbed by a bounded random kick-force, I propose a “direct proof” of the uniqueness of the stationary measure and exponential convergence of solutions to this measure, by showing that the transfer-operator, acting in the space of probability measures given the Kantorovich metric, defines a contraction of this space.
For the entire collection see [Zbl 0990.00046].

MSC:

37H99	Random dynamical systems
35Q30	Navier-Stokes equations