THE BURGERS EQUATION WITH POISSON RANDOM FORCING
成果类型：
Article
署名作者：
Bakhtin, Yuri
署名单位：
University System of Georgia; Georgia Institute of Technology
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/12-AOP747
发表日期：
2013
页码：
2961-2989
关键词：
摘要：
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.