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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-x
Dunlap, 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.
Journal cover image

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