### Abstract

We consider the Burgers equation on the real line with forcing given by Poissonian noise with no periodicity assumption. Under a weak concentration condition on the driving random force, we prove existence and uniqueness of a global solution in a certain class. We describe its basin of attraction that can also be viewed as the main ergodic component for the model. We establish existence and uniqueness of global minimizers associated to the variational principle underlying the dynamics. We also prove the diffusive behavior of the global minimizers on the universal cover in the periodic forcing case.

Original language | English (US) |
---|---|

Pages (from-to) | 2961-2989 |

Number of pages | 29 |

Journal | Annals of Probability |

Volume | 41 |

Issue number | 4 |

DOIs | |

State | Published - 2013 |

### Fingerprint

### Keywords

- Ergodicity
- Global solution
- One force-one solution principle
- One-point attractor
- Poisson point process
- Random environment
- Random forcing
- The Burgers equation
- Variational principle

### ASJC Scopus subject areas

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

*Annals of Probability*,

*41*(4), 2961-2989. https://doi.org/10.1214/12-AOP747

**The burgers equation with poisson random forcing.** / Bakhtin, Yuri.

Research output: Contribution to journal › Article

*Annals of Probability*, vol. 41, no. 4, pp. 2961-2989. https://doi.org/10.1214/12-AOP747

}

TY - JOUR

T1 - The burgers equation with poisson random forcing

AU - Bakhtin, Yuri

PY - 2013

Y1 - 2013

N2 - We consider the Burgers equation on the real line with forcing given by Poissonian noise with no periodicity assumption. Under a weak concentration condition on the driving random force, we prove existence and uniqueness of a global solution in a certain class. We describe its basin of attraction that can also be viewed as the main ergodic component for the model. We establish existence and uniqueness of global minimizers associated to the variational principle underlying the dynamics. We also prove the diffusive behavior of the global minimizers on the universal cover in the periodic forcing case.

AB - We consider the Burgers equation on the real line with forcing given by Poissonian noise with no periodicity assumption. Under a weak concentration condition on the driving random force, we prove existence and uniqueness of a global solution in a certain class. We describe its basin of attraction that can also be viewed as the main ergodic component for the model. We establish existence and uniqueness of global minimizers associated to the variational principle underlying the dynamics. We also prove the diffusive behavior of the global minimizers on the universal cover in the periodic forcing case.

KW - Ergodicity

KW - Global solution

KW - One force-one solution principle

KW - One-point attractor

KW - Poisson point process

KW - Random environment

KW - Random forcing

KW - The Burgers equation

KW - Variational principle

UR - http://www.scopus.com/inward/record.url?scp=84881527316&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84881527316&partnerID=8YFLogxK

U2 - 10.1214/12-AOP747

DO - 10.1214/12-AOP747

M3 - Article

AN - SCOPUS:84881527316

VL - 41

SP - 2961

EP - 2989

JO - Annals of Probability

JF - Annals of Probability

SN - 0091-1798

IS - 4

ER -