Random attractors for the 3d stochastic navier-stokes equation with multiplicative white noise

Abstract

The random attractor to the stochastic 3D Navier-Stokes equation will be studied. In the first part we formulate an existence theorem for attractors of non-autonomous dynamical systems on a bundle of metric spaces. Using this theorem we can prove the existence of an attractor for the 3D Navier-Stokes equation with multiplicative white noise. In addition we prove that this attractor is a random multi-function