Two dimensional nonlinear Schr\"odinger equation with spatial white noise potential and fourth order nonlinearity - ENS de Lyon - École normale supérieure de Lyon
Preprints, Working Papers, ... Year : 2020

Two dimensional nonlinear Schr\"odinger equation with spatial white noise potential and fourth order nonlinearity

Abstract

We consider NLS on $\T^2$ with multiplicative spatial white noise and nonlinearity between cubic and quartic. We prove global existence, uniqueness and convergence almost surely of solutions to a family of properly regularized and renormalized approximating equations. In particular we extend a previous result by A. Debussche and H. Weber available in the cubic and sub-cubic setting.

Dates and versions

ensl-04829806 , version 1 (10-12-2024)

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Cite

Nikolay Tzvetkov, Nicola Visciglia. Two dimensional nonlinear Schr\"odinger equation with spatial white noise potential and fourth order nonlinearity. 2024. ⟨ensl-04829806⟩
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