Kuksin, Sergei; Shirikyan, Armen Ergodicity for the randomly forced 2D Navier-Stokes equations. (English) Zbl 1013.37046 Math. Phys. Anal. Geom. 4, No. 2, 147-195 (2001). Summary: We study space-periodic 2D Navier-Stokes equations perturbed by an unbounded random kick-force. It is assumed that Fourier coefficients of the kicks are independent random variables all of whose moments are bounded and that the distributions of the first \(N_0\) coefficients (where \(N_0\) is a sufficiently large integer) have positive densities against the Lebesgue measure. We treat the equation as a random dynamical system in the space of square integrable divergence-free vector fields. We prove that this dynamical system has a unique stationary measure and study its ergodic properties. Cited in 1 ReviewCited in 30 Documents MSC: 37H15 Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents 35Q30 Navier-Stokes equations Keywords:kick-force; stationary measure; random dynamical system; Ruelle-Perron-Frobenius theorem PDFBibTeX XMLCite \textit{S. Kuksin} and \textit{A. Shirikyan}, Math. Phys. Anal. Geom. 4, No. 2, 147--195 (2001; Zbl 1013.37046) Full Text: DOI