Stochastic dissipative PDE ’ s and Gibbs measures

  title={Stochastic dissipative PDE ’ s and Gibbs measures},
  author={Sergei Kuksin and Armen Shirikyan},
We study a class of dissipative nonlinear PDE’s forced by a random force η(t, x), with the space variable x varying in a bounded domain. The class contains the 2D Navier–Stokes equations (under periodic or Dirichlet boundary conditions), and the forces we consider are those common in statistical hydrodynamics: they are random fields smooth in x and stationary, short-correlated in time t. In this paper, we confine ourselves to “kick forces” of the form 
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