Stochastic dissipative PDE’s and Gibbs measures

We study a class of dissipative nonlinear PDE’s forced by a random force ηω(t, x), with the space variable x varying in a bounded domain. The class contains the 2D Navier–Stokes equations (under periodic or Dirich-let boundary conditions), and the forces we consider are those common in statistical hydrodynamics: they are random fields smooth in x and sta-tionary, short-correlated in time t. In this paper, we confine ourselves to “kick forces ” of the form η ω(t, x)