## Stationary solutions to the stochastic burgers equation on the line

Publication
, Journal Article

Dunlap, A; Graham, C; Ryzhik, L

Published in: Communications in Mathematical Physics

March 1, 2021

We consider invariant measures for the stochastic Burgers equation on $\mathbb{R}$, forced by the derivative of a spacetime-homogeneous Gaussian noise that is white in time and smooth in space. An invariant measure is indecomposable, or extremal, if it cannot be represented as a convex combination of other invariant measures. We show that for each $a\in\mathbb{R}$, there is a unique indecomposable law of a spacetime-stationary solution with mean $a$, in a suitable function space. We also show that solutions starting from spatially-decaying perturbations of mean-$a$ periodic functions converge in law to the extremal space-time stationary solution with mean $a$ as time goes to infinity.

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## Published In

Communications in Mathematical Physics

## DOI

## EISSN

1432-0916

## ISSN

0010-3616

## Publication Date

March 1, 2021

## Volume

382

## Issue

2

## Start / End Page

875 / 949

## Related Subject Headings

- Mathematical Physics
- 5107 Particle and high energy physics
- 4904 Pure mathematics
- 4902 Mathematical physics
- 0206 Quantum Physics
- 0105 Mathematical Physics
- 0101 Pure Mathematics

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Dunlap, A., Graham, C., & Ryzhik, L. (2021). Stationary solutions to the stochastic burgers equation on the line.

*Communications in Mathematical Physics*,*382*(2), 875–949. https://doi.org/10.1007/s00220-021-04025-xDunlap, Alexander, Cole Graham, and Lenya Ryzhik. “Stationary solutions to the stochastic burgers equation on the line.”

*Communications in Mathematical Physics*382, no. 2 (March 1, 2021): 875–949. https://doi.org/10.1007/s00220-021-04025-x.Dunlap A, Graham C, Ryzhik L. Stationary solutions to the stochastic burgers equation on the line. Communications in Mathematical Physics. 2021 Mar 1;382(2):875–949.

Dunlap, Alexander, et al. “Stationary solutions to the stochastic burgers equation on the line.”

*Communications in Mathematical Physics*, vol. 382, no. 2, Mar. 2021, pp. 875–949.*Manual*, doi:10.1007/s00220-021-04025-x.Dunlap A, Graham C, Ryzhik L. Stationary solutions to the stochastic burgers equation on the line. Communications in Mathematical Physics. 2021 Mar 1;382(2):875–949.

## Published In

Communications in Mathematical Physics

## DOI

## EISSN

1432-0916

## ISSN

0010-3616

## Publication Date

March 1, 2021

## Volume

382

## Issue

2

## Start / End Page

875 / 949

## Related Subject Headings

- Mathematical Physics
- 5107 Particle and high energy physics
- 4904 Pure mathematics
- 4902 Mathematical physics
- 0206 Quantum Physics
- 0105 Mathematical Physics
- 0101 Pure Mathematics