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

Publication
, Journal Article

Dunlap, A

Published in: Nonlinearity

October 1, 2020

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.

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## Published In

Nonlinearity

## DOI

## EISSN

1361-6544

## ISSN

0951-7715

## Publication Date

October 1, 2020

## Volume

33

## Issue

12

## Start / End Page

6480 / 6501

## Related Subject Headings

- General Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics

### Citation

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MLA

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Dunlap, A. (2020). Existence of stationary stochastic Burgers evolutions on $\mathbf{R}^2$ and $\mathbf{R}^3$.

*Nonlinearity*,*33*(12), 6480–6501. https://doi.org/10.1088/1361-6544/aba50aDunlap, Alexander. “Existence of stationary stochastic Burgers evolutions on $\mathbf{R}^2$ and $\mathbf{R}^3$.”

*Nonlinearity*33, no. 12 (October 1, 2020): 6480–6501. https://doi.org/10.1088/1361-6544/aba50a.Dunlap A. Existence of stationary stochastic Burgers evolutions on $\mathbf{R}^2$ and $\mathbf{R}^3$. Nonlinearity. 2020 Oct 1;33(12):6480–501.

Dunlap, Alexander. “Existence of stationary stochastic Burgers evolutions on $\mathbf{R}^2$ and $\mathbf{R}^3$.”

*Nonlinearity*, vol. 33, no. 12, Oct. 2020, pp. 6480–501.*Manual*, doi:10.1088/1361-6544/aba50a.Dunlap A. Existence of stationary stochastic Burgers evolutions on $\mathbf{R}^2$ and $\mathbf{R}^3$. Nonlinearity. 2020 Oct 1;33(12):6480–6501.

## Published In

Nonlinearity

## DOI

## EISSN

1361-6544

## ISSN

0951-7715

## Publication Date

October 1, 2020

## Volume

33

## Issue

12

## Start / End Page

6480 / 6501

## Related Subject Headings

- General Mathematics
- 4904 Pure mathematics
- 4901 Applied mathematics
- 0102 Applied Mathematics