Random Dynamical Systems and 

Stochastic Partial Differential Equations

 

Abstract

The theory of random dynamical systems allows us to study the long-time behavior of systems under the influence of random perturbations. Using the tools of this theory we will investigate stochastic partial differential equation. In particular, we will show that the 2D stochastic Navier Stokes equation has a random fixed point if the viscosity parameter is large. For the quasigeostrophic equation with noise on the boundary we can show the existence of a random attractor. We will also apply one concept of finite dimensionality to stochastic two-layer system.