Burgers equation with Poisson random forcing

Details Burgers equation with Poisson random forcing Burgers equation with Poisson random forcing

2011-09-26

arxiv.org/abs/1109.5668v1

Mathematics

Probability

28 pages, 1 figure

Scientific paper

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.

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