The author considers Navier-Stokes systems (in any dimension) where the external forces are replaced by random ones of white-noise type (adapted in particular to the dimension). By formulating the problem in suitable functional spaces, the systems dealt with are stochastic (ordinary) differential equations in infinite dimensions. On one hand, the existence of solutions of such equations and, on the other, the existence of invariant measures associated to such solutions is proved.
A joint work of the author with S. Albeverio is announced where this problem is treated in the two-dimensional case. There the invariant measures are constructed explicitly (they are Gaussian measures).