Space-time stationary solutions for the Burgers equation

@article{Bakhtin2012SpacetimeSS,
  title={Space-time stationary solutions for the Burgers equation},
  author={Yuri Bakhtin and Eric A. Cator and Konstantin Khanin},
  journal={Journal of the American Mathematical Society},
  year={2012},
  volume={27},
  pages={193-238}
}
We construct space-time stationary solutions of the 1D Burgers equation with random forcing in the absence of periodicity or any other compactness assumptions. More precisely, for the forcing given by a homogeneous Poissonian point field in space-time we prove that there is a unique global solution with any prescribed average ve- locity. These global solutions serve as one-point random attractors for the infinite-dimensional dynamical system associated to solutions to the Cauchy problem. The… 
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