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Ergodicity for the randomly forced 2D Navier-Stokes equations. (English) Zbl 1013.37046
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.

MSC:
37H15 Random dynamical systems aspects of multiplicative ergodic theory, Lyapunov exponents
35Q30 Navier-Stokes equations
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