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

2023/01/25 by Debussche, Arnaud, Liu, Ruoyuan, Tzvetkov, Nikolay +1
#35Q55 #60H15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Probability (math.PR)

paper · doi:10.48550/arxiv.2301.10825

Abstract

We 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 (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.

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