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Global well-posedness of the 2D nonlinear Schrödinger equation with multiplicative spatial white noise on the full
Arnaud Debussche1, Ruoyuan Liu2, Nikolay Tzvetkov3
1CNRS, IRMAR - UMR 6625, Univ Rennes, 35000 Rennes, France.
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 (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.
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