On Approximate Inertial Manifolds for Stochastic Navier-Stokes Equations

The stochastic approximate inertial manifold is constructed for 2D Navier-Stokes equations with random initial data and excited by additive white noise. We estimate the size of the corresponding attracting neighborhood for this manifold. Our consideration relies on some additional information on the nonlinear term in Navier-Stokes equations.