Global well-posedness of the 2D nonlinear Schrödinger equation with multiplicative spatial white noise on the full space-Reference-Cited by-同舟云学术

Global well-posedness of the 2D nonlinear Schrödinger equation with multiplicative spatial white noise on the full space

Published:2024-06-22 Issue:3-4 Volume:189 Page:1161-1218
ISSN:0178-8051
Container-title:Probability Theory and Related Fields
language:en
Short-container-title:Probab. Theory Relat. Fields

Author:

Debussche Arnaud,Liu Ruoyuan,Tzvetkov Nikolay,Visciglia Nicola

Abstract

AbstractWe consider the nonlinear Schrödinger 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 Labbé (Electron Commun Probab 20(43):11, 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 (Nonlinearity 32(4):1147–1174, 2019) with a sub-quadratic nonlinearity.

Funder

Agence Nationale de la Recherche

French government "Investissernents d’Avenir" program

European Research Council

Ministero dell’Istruzione, dell’Università e della Ricerca

Università di Pisa

Publisher

Springer Science and Business Media LLC

Link

https://link.springer.com/content/pdf/10.1007/s00440-024-01288-y.pdf

Reference44 articles.

1. Allez, R., Chouk, K.: The continuous Anderson hamiltonian in dimension two. arXiv:1511.02718 [math.PR]

2. Bahouri, H., Chemin, J.-Y., Danchin, R.: Fourier analysis and nonlinear partial differential equations. Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], p. 343. Springer, Heidelberg (2011). xvi+523 pp. ISBN: 978-3-642-16829-1

3. Bailleul, I., Dang, N.V., Mouzard, A.: Analysis of the Anderson operator. arXiv:2201.04705 [math.PR]

4. Bourdaud, G.: Sur les opérateurs pseudo-différentiels à coefficients peu règuliers. Habilitation thesis, Université de Paris-Sud, Paris (1983)

5. Bourdaud, G.: Fonctions qui opèrent sur les espaces de Besov et de Triebel. Ann. Inst. Henri Poincaré, Anal. Non Linéaire 10(4), 413–422 (1993)