In my lectures I shall present various results on dissipative nonlinear PDEs, perturbed by a random force. As a function of time the force will be either a kick-process, or a white noise. In the first part of the lectures I shall discuss the existence and uniqueness of solutions, the Ito formula and basic properties of the Markov processes which these equations define in functional spaces. The second part will be dedicated to the problem of existence and uniqueness of the stationary measure and to the study of asymptotical properties of solutions. Finally, in the third part I shall present some results on the small-viscosity limit for solutions of equations, when the force is scaled accordingly. My main example will be the randomly perturbed 2D Navier-Stokes system which describes the 2D statistical hydrodynamics (and the 2D turbulence as its part). Accordingly, I shall systematically discuss relevance of the results obtained for this field of hydrodynamics.
Zeit: Donnerstag, 13-15 Uhr
Ort: HG G 43 (Hermann-Weyl-Zimmer)