Existence of stationary stochastic Burgers evolutions on R 2 and R 3 * *The author was partially supported by the NSF Graduate Research Fellowship Program under Grant DGE-1147470.

Abstract

We prove that the stochastic Burgers equation on R d , d < 4, forced by gradient noise that is white in time and smooth in space, admits spacetime-stationary solutions. These solutions are thus the gradients of solutions to the KPZ equation on R d with stationary gradients. The proof works by proving tightness of the time-averaged laws of the solutions in an appropriate weighted space.