The Burgers equation with Poisson random forcing
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.
Keywords
Cite
@article{arxiv.1109.5668,
title = {The Burgers equation with Poisson random forcing},
author = {Yuri Bakhtin},
journal= {arXiv preprint arXiv:1109.5668},
year = {2013}
}
Comments
Published in at http://dx.doi.org/10.1214/12-AOP747 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)