Invariant Measures for NLS in Infinite Volume

@article{Bourgain2000InvariantMF,
  title={Invariant Measures for NLS in Infinite Volume},
  author={Jean Bourgain},
  journal={Communications in Mathematical Physics},
  year={2000},
  volume={210},
  pages={605-620}
}
Abstract: We study Gibbs-measures and invariant dynamics for 1D-defocusing NLS iut+uxx−ρu−u|u|p−2=0 when the period L→∞. For all p<∞ weak solutions are typically Hölder continuous on bounded space-time regions. If p≤ 4, uniqueness and continuous dependence on the initial data may be shown. 

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