On the stochastic nonlinear Schrödinger equations at critical regularities.

Tadahiro Oh; Mamoru Okamoto

doi:10.1007/s40072-019-00163-5

On the stochastic nonlinear Schrödinger equations at critical regularities.

Tadahiro Oh, Mamoru Okamoto

School of Mathematics

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

Abstract

We consider the Cauchy problem for the defocusing stochastic nonlinear Schrödinger equations (SNLS) with an additive noise in the mass-critical and energy-critical settings. By adapting the probabilistic perturbation argument employed in the context of the random data Cauchy theory by the first author with Bényi and Pocovnicu (2015) to the current stochastic PDE setting, we present a concise argument to establish global well-posedness of the mass-critical and energy-critical SNLS.

Original language	English
Pages (from-to)	869–894
Number of pages	26
Journal	Stochastics and Partial Differential Equations: Analysis and Computations
Volume	8
Early online date	3 Jan 2020
DOIs	https://doi.org/10.1007/s40072-019-00163-5
Publication status	Published - 31 Dec 2020

Keywords

stochastic nonlinear Schrödinger equation
global well-posedness
mass-critical
energy-critical
perturbation theory

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10.1007/s40072-019-00163-5

2020SPDE_SNLSFinal published version, 458 KB

ProbDynDispEq - Probabilistic and Dynamical Study of Nonlinear Dispersive Equations
Oh, T.
EU government bodies
1/03/15 → 29/02/20
Project: Research

Cite this

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abstract = "We consider the Cauchy problem for the defocusing stochastic nonlinear Schr{\"o}dinger equations (SNLS) with an additive noise in the mass-critical and energy-critical settings. By adapting the probabilistic perturbation argument employed in the context of the random data Cauchy theory by the first author with B{\'e}nyi and Pocovnicu (2015) to the current stochastic PDE setting, we present a concise argument to establish global well-posedness of the mass-critical and energy-critical SNLS. ",

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AU - Okamoto, Mamoru

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N2 - We consider the Cauchy problem for the defocusing stochastic nonlinear Schrödinger equations (SNLS) with an additive noise in the mass-critical and energy-critical settings. By adapting the probabilistic perturbation argument employed in the context of the random data Cauchy theory by the first author with Bényi and Pocovnicu (2015) to the current stochastic PDE setting, we present a concise argument to establish global well-posedness of the mass-critical and energy-critical SNLS.

AB - We consider the Cauchy problem for the defocusing stochastic nonlinear Schrödinger equations (SNLS) with an additive noise in the mass-critical and energy-critical settings. By adapting the probabilistic perturbation argument employed in the context of the random data Cauchy theory by the first author with Bényi and Pocovnicu (2015) to the current stochastic PDE setting, we present a concise argument to establish global well-posedness of the mass-critical and energy-critical SNLS.

KW - stochastic nonlinear Schrödinger equation

KW - global well-posedness

KW - mass-critical

KW - energy-critical

KW - perturbation theory

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DO - 10.1007/s40072-019-00163-5

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JO - Stochastics and Partial Differential Equations: Analysis and Computations

JF - Stochastics and Partial Differential Equations: Analysis and Computations

SN - 2194-0401

ER -

On the stochastic nonlinear Schrödinger equations at critical regularities.

Abstract

Keywords

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Projects

ProbDynDispEq - Probabilistic and Dynamical Study of Nonlinear Dispersive Equations

Cite this