Transport by Time Dependent Stationary Flow

Abstract:

We consider transport properties for Gaussian, stationary, divergence free, random velocity fields in ℝ², which are Markov in time. We prove the existence of effective diffusivity. We also obtain its full asymptotics in the case of short time correlations, on a fully rigorous level. The main regularity assumption is that almost every realization of the random velocity field should be continuous in space and time, and Lipschitz continuous in space.