Invariant measures for the defocusing Nonlinear Schrödinger equation
Tzvetkov, Nikolay
Annales de l'Institut Fourier, Volume 58 (2008), p. 2543-2604 / Harvested from Numdam
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We prove the existence and the invariance of a Gibbs measure associated to the defocusing sub-quintic Nonlinear Schrödinger equations on the disc of the plane ℝ 2 . We also prove an estimate giving some intuition to what may happen in 3 dimensions.

On démontre l’existence et l’invariance d’une mesure de Gibbs par le flot de l’équation de Schrödinger non linéaire posée sur le disque du plan ℝ 2 . On démontre également une estimée qui donne une idée de ce qui pourrait arriver en dimension 3.

Published online : 2008-01-01
DOI : https://doi.org/10.5802/aif.2422
Classification:  35Q55,  35BXX,  37K05,  37L50,  81Q20
Keywords: Nonlinear Schrödinger, eigenfunctions, dispersive equations, invariant measures 
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     author = {Tzvetkov, Nikolay},
     title = {Invariant measures for the defocusing Nonlinear Schr\"odinger equation},
     journal = {Annales de l'Institut Fourier},
     volume = {58},
     year = {2008},
     pages = {2543-2604},
     doi = {10.5802/aif.2422},
     zbl = {1171.35116},
     mrnumber = {2498359},
     language = {en},
     url = {http://dml.mathdoc.fr/item/AIF_2008__58_7_2543_0}
}

Tzvetkov, Nikolay. Invariant measures for the defocusing Nonlinear Schrödinger equation. Annales de l'Institut Fourier, Volume 58 (2008) pp. 2543-2604. doi : 10.5802/aif.2422. http://gdmltest.u-ga.fr/item/AIF_2008__58_7_2543_0/

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