Solution to the stochastic Schr\"odinger equation on the full space

Abstract : We here show how the methods recently applied by [DW16] to solve the stochastic nonlinear Schr\"odinger 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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https://hal.archives-ouvertes.fr/hal-01579115
Contributor : Marie-Annick Guillemer <>
Submitted on : Wednesday, August 30, 2017 - 2:35:23 PM
Last modification on : Sunday, March 17, 2019 - 1:20:33 AM

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Arnaud Debussche, Jörg Martin. Solution to the stochastic Schr\"odinger equation on the full space. Nonlinearity, IOP Publishing, 2019, 32 (4), pp.1147-1174. ⟨10.1088/1361-6544/aaf50e⟩. ⟨hal-01579115⟩

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