Stochastic nonlinear Schrödinger equations on tori

Kelvin Cheung; Razvan Mosincat

doi:10.1007/s40072-018-0125-x

Stochastic nonlinear Schrödinger equations on tori

Kelvin Cheung, Razvan Mosincat

School of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We consider the stochastic nonlinear Schrödinger equations (SNLS) posed on d-dimensional tori with either additive or multiplicative stochastic forcing. In particular, for the one-dimensional cubic SNLS, we prove global well-posedness in L2(T) . As for other power-type nonlinearities, namely (i) (super)quintic when d=1 and (ii) (super)cubic when d≥2 , we prove local well-posedness in all scaling-subcritical Sobolev spaces and global well-posedness in the energy space for the defocusing, energy-subcritical problems.

Original language	English
Pages (from-to)	169-208
Number of pages	40
Journal	Stochastics and Partial Differential Equations: Analysis and Computations
Volume	7
Issue number	2
Early online date	29 Aug 2018
DOIs	https://doi.org/10.1007/s40072-018-0125-x
Publication status	Published - 30 Jun 2019

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abstract = "We consider the stochastic nonlinear Schr{\"o}dinger equations (SNLS) posed on d-dimensional tori with either additive or multiplicative stochastic forcing. In particular, for the one-dimensional cubic SNLS, we prove global well-posedness in L2(T) . As for other power-type nonlinearities, namely (i) (super)quintic when d=1 and (ii) (super)cubic when d≥2 , we prove local well-posedness in all scaling-subcritical Sobolev spaces and global well-posedness in the energy space for the defocusing, energy-subcritical problems.",

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AU - Mosincat, Razvan

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N2 - We consider the stochastic nonlinear Schrödinger equations (SNLS) posed on d-dimensional tori with either additive or multiplicative stochastic forcing. In particular, for the one-dimensional cubic SNLS, we prove global well-posedness in L2(T) . As for other power-type nonlinearities, namely (i) (super)quintic when d=1 and (ii) (super)cubic when d≥2 , we prove local well-posedness in all scaling-subcritical Sobolev spaces and global well-posedness in the energy space for the defocusing, energy-subcritical problems.

AB - We consider the stochastic nonlinear Schrödinger equations (SNLS) posed on d-dimensional tori with either additive or multiplicative stochastic forcing. In particular, for the one-dimensional cubic SNLS, we prove global well-posedness in L2(T) . As for other power-type nonlinearities, namely (i) (super)quintic when d=1 and (ii) (super)cubic when d≥2 , we prove local well-posedness in all scaling-subcritical Sobolev spaces and global well-posedness in the energy space for the defocusing, energy-subcritical problems.

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DO - 10.1007/s40072-018-0125-x

M3 - Article

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JO - Stochastics and Partial Differential Equations: Analysis and Computations

JF - Stochastics and Partial Differential Equations: Analysis and Computations

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ER -

Stochastic nonlinear Schrödinger equations on tori

Abstract

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