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arXiv · 1707.06431

Solution to the stochastic Schrödinger equation on the full space

Arnaud Debussche·Jörg Martin
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Abstract

We here show how the methods recently applied by [DW16] to solve the stochastic nonlinear Schrödinger equation on $\mathbb{T}^2$ can be enhanced to yield solutions on $\mathbb{R}^2$ if the non-linearity is weak enough. We prove that the solutions remains localized on compact time intervals which allows us to apply energy methods on the full space.

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Arnaud Debussche, Jörg Martin. 2017-07-20. Solution to the stochastic Schrödinger equation on the full space. https://arxiv.org/abs/1707.06431

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