Global well-posedness of the 2D nonlinear Schr\"odinger equation with multiplicative spatial white noise on the full space - ENS de Lyon - École normale supérieure de Lyon Accéder directement au contenu
Pré-Publication, Document De Travail Année : 2024

Global well-posedness of the 2D nonlinear Schr\"odinger equation with multiplicative spatial white noise on the full space

Arnaud Debussche
  • Fonction : Auteur
Ruoyuan Liu
  • Fonction : Auteur
Nicola Visciglia
  • Fonction : Auteur

Résumé

We consider the nonlinear Schr\"odinger equation with multiplicative spatial white noise and an arbitrary polynomial nonlinearity on the two-dimensional full space domain. We prove global well-posedness by using a gauge-transform introduced by Hairer and Labb\'e (2015) and constructing the solution as a limit of solutions to a family of approximating equations. This paper extends a previous result by Debussche and Martin (2019) with a sub-quadratic nonlinearity.

Dates et versions

ensl-04410028 , version 1 (22-01-2024)

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Arnaud Debussche, Ruoyuan Liu, Nikolay Tzvetkov, Nicola Visciglia. Global well-posedness of the 2D nonlinear Schr\"odinger equation with multiplicative spatial white noise on the full space. 2024. ⟨ensl-04410028⟩
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