## Electronic Journal of Probability

- Electron. J. Probab.
- Volume 21, Number (2016), paper no. 37, 50 pp.

### Inviscid Burgers equation with random kick forcing in noncompact setting

#### Abstract

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.

#### Article information

**Source**

Electron. J. Probab. Volume 21, Number (2016), paper no. 37, 50 pp.

**Dates**

Received: 7 July 2015

Accepted: 12 May 2016

First available in Project Euclid: 19 May 2016

**Permanent link to this document**

https://projecteuclid.org/euclid.ejp/1463683782

**Digital Object Identifier**

doi:10.1214/16-EJP4413

**Subjects**

Primary: 37L40: Invariant measures 37L55: Infinite-dimensional random dynamical systems; stochastic equations [See also 35R60, 60H10, 60H15] 35R60: Partial differential equations with randomness, stochastic partial differential equations [See also 60H15] 37H99: None of the above, but in this section 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60G55: Point processes

**Keywords**

SPDE Burgers equation last passage percolation invariant distributions Busemann functions One Force – One Solution Principle

**Rights**

Creative Commons Attribution 4.0 International License.

#### Citation

Bakhtin, Yuri. Inviscid Burgers equation with random kick forcing in noncompact setting. Electron. J. Probab. 21 (2016), paper no. 37, 50 pp. doi:10.1214/16-EJP4413. https://projecteuclid.org/euclid.ejp/1463683782.