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 N0 coefficients (where N0 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. © 2001 Kluwer Academic Publishers.
Original language | English |
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Pages (from-to) | 147-195 |
Number of pages | 49 |
Journal | Mathematical Physics, Analysis and Geometry |
Volume | 4 |
Issue number | 2 |
DOIs | |
Publication status | Published - 2001 |
Keywords
- Kick-force
- Navier-Stokes equations
- Random dynamical system
- Ruelle-Perron-Frobenius theorem
- Stationary measure