### Abstract

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

Article number | 1406.5660 |

Journal | arXiv |

State | Published - Jun 22 2014 |

### Fingerprint

### Keywords

- math.PR
- math.AP
- math.DS
- 37L40, 37L55, 35R60, 37H99, 60K35, 60G55

### Cite this

*arXiv*, [1406.5660].

**Inviscid Burgers equation with random kick forcing in noncompact setting.** / Bakhtin, Yury.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Inviscid Burgers equation with random kick forcing in noncompact setting

AU - Bakhtin, Yury

N1 - 58 pages. This is an extension of work in arXiv:1205.6721 to the kick-forcing setting. In this version, instead of Kesten's concentration inequality, the more basic Azuma--Hoeffding inequality is used in Section 5

PY - 2014/6/22

Y1 - 2014/6/22

N2 - We develop ergodic theory of the inviscid Burgers equation with random kick forcing in noncompact setting. The results are parallel to those in our recent work on the Burgers equation with Poissonian forcing. However, the analysis based on the study of one-sided minimizers of the relevant action is different. In contrast with previous work, finite time coalescence of the minimizers does not hold, and hyperbolicity (exponential convergence of minimizers in reverse time) is not known. In order to establish a One Force --- One Solution principle on each ergodic component, we use an extremely soft method to prove a weakened hyperbolicity property and to construct Busemann functions along appropriate subsequences.

AB - We develop ergodic theory of the inviscid Burgers equation with random kick forcing in noncompact setting. The results are parallel to those in our recent work on the Burgers equation with Poissonian forcing. However, the analysis based on the study of one-sided minimizers of the relevant action is different. In contrast with previous work, finite time coalescence of the minimizers does not hold, and hyperbolicity (exponential convergence of minimizers in reverse time) is not known. In order to establish a One Force --- One Solution principle on each ergodic component, we use an extremely soft method to prove a weakened hyperbolicity property and to construct Busemann functions along appropriate subsequences.

KW - math.PR

KW - math.AP

KW - math.DS

KW - 37L40, 37L55, 35R60, 37H99, 60K35, 60G55

M3 - Article

JO - arXiv

JF - arXiv

M1 - 1406.5660

ER -