Invariant measures for Burgers equation with stochastic forcing

@article{Weinan2000InvariantMF,
  title={Invariant measures for Burgers equation with stochastic forcing},
  author={E Weinan and Konstantin Khanin and Alexandre Mazel and Yakov G. Sinai},
  journal={Annals of Mathematics},
  year={2000},
  volume={151},
  pages={877-960}
}
In this paper we study the following Burgers equation du/dt + d/dx (u^2/2) = epsilon d^2u/dx^2 + f(x,t) where f(x,t)=dF/dx(x,t) is a random forcing function, which is periodic in x and white noise in t. We prove the existence and uniqueness of an invariant measure by establishing a ``one force, one solution'' principle, namely that for almost every realization of the force, there is a unique distinguished solution that exists for the time interval (-infty, +infty) and this solution attracts… 
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