### 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 |

### 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

## Fingerprint Dive into the research topics of 'The burgers equation with poisson random forcing'. Together they form a unique fingerprint.

## Cite this

Bakhtin, Y. (2013). The burgers equation with poisson random forcing.

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