• DOI:10.1007/BF02099299
Corpus ID: 53447933

Periodic nonlinear Schrödinger equation and invariant measures

@article{Bourgain1994PeriodicNS,
  title={Periodic nonlinear Schr{\"o}dinger equation and invariant measures},
  author={J. Bourgain},
  journal={Communications in Mathematical Physics},
  year={1994},
  volume={166},
  pages={1-26}
}

J. Bourgain

Published 1994

Mathematics

Communications in Mathematical Physics

AbstractIn this paper we continue some investigations on the periodic NLSEiuu +iuxx +u|u|p-2 (p≦6) started in [LRS]. We prove that the equation is globally wellposed for a set of data Φ of full normalized Gibbs measrue $$e^{ - \beta H(\phi )} Hd\phi (x),H(\phi ) = \tfrac{1}{2}\int {\left| {\phi '} \right|^2 - \tfrac{1}{p}\int {\left| \phi \right|p} } $$ (after suitableL2-truncation). The set and the measure are invariant under the flow. The proof of a similar result for the KdV and modified… CONTINUE READING

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