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arXiv · 2301.10825

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

Arnaud Debussche·Ruoyuan Liu·Nikolay Tzvetkov·Nicola Visciglia
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Abstract

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.

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Arnaud Debussche, Ruoyuan Liu, Nikolay Tzvetkov, Nicola Visciglia. 2023-01-25. Global well-posedness of the 2D nonlinear Schr\"odinger equation with multiplicative spatial white noise on the full space. https://arxiv.org/abs/2301.10825

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