Existence of stationary stochastic Burgers evolutions on ${\mathbf{R}}^2$ and ${\mathbf{R}}^3$

Abstract

We prove that the stochastic Burgers equation on ${\mathbf{R}}^d$, $d<4$, 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 ${\mathbf{R}}^d$ with stationary gradients. The proof works by proving tightness of the time-averaged laws of the solutions in an appropriate weighted space.

16 pages

References in corpus (2)

• The Edwards-Wilkinson limit of the random heat equation in dimensions three and higher
• Stationary solutions to the stochastic Burgers equation on the line

Cited by in corpus (3)

• Local KPZ behavior under arbitrary scaling limits
• Invariant measures for stochastic conservation laws on the line
• Dynamic polymers: invariant measures and ordering by noise