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We consider the nonlinear Schr\"odinger equation with multiplicative spatialwhite noise and an arbitrary polynomial nonlinearity on the two-dimensionalfull space domain. We prove global well-posedness by using a gauge-transformintroduced by Hairer and Labb\'e (2015) and constructing the solution as alimit of solutions to a family of approximating equations. This paper extends aprevious result by Debussche and Martin (2019) with a sub-quadraticnonlinearity.

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