Abstract
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.
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