# 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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On the invariant measure for the nonlinear Schrόdinger equation