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

Autor:	Debussche, Arnaud, Liu, Ruoyuan, Tzvetkov, Nikolay, Visciglia, Nicola
Rok vydání:	2023
Předmět:	Mathematics - Analysis of PDEs Mathematics - Probability 35Q55 60H15
Druh dokumentu:	Working Paper
Popis:	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. Comment: 45 pages. We now prove an almost sure convergence of the approximating solutions
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2301.10825 Zobrazit plný text záznamu View this record from Arxiv