Irreducibility of the 3-D Stochastic Navier–Stokes Equation

A 3-dimensional Navier–Stokes equation with random force is investigated. A form of irreducibility, of interest in ergodic theory, is proved, under a full noise assumption. The basic tool is the fact that, even if the equation is a priori non-well-posed, the solutions depend continuously on the noise around regular solutions.