Mixing for the Burgers equation driven by a localised two-dimensional stochastic forcing

Abstract

We consider the one-dimensional Burgers equation perturbed by a stochastic forcing, which is assumed to be white in time and localised and low-dimensional in space. We establish a mixing property for the Markov process associated with the problem in question. The proof is based on a general criterion for mixing and a recent result on global approximate controllability to trajectories for damped conservation laws.