Global Well-Posedness of the 4-D Energy-Critical Stochastic Nonlinear Schrödinger Equations with Non-Vanishing Boundary Condition

Kelvin Cheung; Guopeng Li

doi:10.1619/fesi.65.287

Global Well-Posedness of the 4-D Energy-Critical Stochastic Nonlinear Schrödinger Equations with Non-Vanishing Boundary Condition

Kelvin Cheung
, Guopeng Li

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

4 Citations (Scopus)

Abstract

We consider the energy-critical stochastic cubic nonlinear Schrödinger equation on R⁴ with additive noise, and with the non-vanishing boundary conditions at spatial infinity. By viewing this equation as a perturbation to the energy-critical cubic nonlinear Schrödinger equation on R⁴, we prove global well-posedness in the energy space. Moreover, we establish unconditional uniqueness of solutions in the energy space.

Original language	English
Pages (from-to)	287-309
Number of pages	23
Journal	Funkcialaj Ekvacioj
Volume	65
Issue number	3
DOIs	https://doi.org/10.1619/fesi.65.287
Publication status	Published - 2022
Externally published	Yes

Keywords

Energy-critical
Global well-posedness
Non-vanishing boundary condition
Perturbation theory
Stochastic nonlinear Schrödinger equation

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10.1619/fesi.65.287

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title = "Global Well-Posedness of the 4-D Energy-Critical Stochastic Nonlinear Schr{\"o}dinger Equations with Non-Vanishing Boundary Condition",

abstract = "We consider the energy-critical stochastic cubic nonlinear Schr{\"o}dinger equation on R4 with additive noise, and with the non-vanishing boundary conditions at spatial infinity. By viewing this equation as a perturbation to the energy-critical cubic nonlinear Schr{\"o}dinger equation on R4, we prove global well-posedness in the energy space. Moreover, we establish unconditional uniqueness of solutions in the energy space.",

keywords = "Energy-critical, Global well-posedness, Non-vanishing boundary condition, Perturbation theory, Stochastic nonlinear Schr{\"o}dinger equation",

author = "Kelvin Cheung and Guopeng Li",

year = "2022",

doi = "10.1619/fesi.65.287",

language = "English",

volume = "65",

pages = "287--309",

journal = "Funkcialaj Ekvacioj",

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T1 - Global Well-Posedness of the 4-D Energy-Critical Stochastic Nonlinear Schrödinger Equations with Non-Vanishing Boundary Condition

AU - Cheung, Kelvin

AU - Li, Guopeng

PY - 2022

Y1 - 2022

N2 - We consider the energy-critical stochastic cubic nonlinear Schrödinger equation on R4 with additive noise, and with the non-vanishing boundary conditions at spatial infinity. By viewing this equation as a perturbation to the energy-critical cubic nonlinear Schrödinger equation on R4, we prove global well-posedness in the energy space. Moreover, we establish unconditional uniqueness of solutions in the energy space.

AB - We consider the energy-critical stochastic cubic nonlinear Schrödinger equation on R4 with additive noise, and with the non-vanishing boundary conditions at spatial infinity. By viewing this equation as a perturbation to the energy-critical cubic nonlinear Schrödinger equation on R4, we prove global well-posedness in the energy space. Moreover, we establish unconditional uniqueness of solutions in the energy space.

KW - Energy-critical

KW - Global well-posedness

KW - Non-vanishing boundary condition

KW - Perturbation theory

KW - Stochastic nonlinear Schrödinger equation

UR - https://www.scopus.com/pages/publications/85142601524

U2 - 10.1619/fesi.65.287

DO - 10.1619/fesi.65.287

M3 - Article

AN - SCOPUS:85142601524

SN - 0532-8721

VL - 65

SP - 287

EP - 309

JO - Funkcialaj Ekvacioj

JF - Funkcialaj Ekvacioj

IS - 3

ER -

Global Well-Posedness of the 4-D Energy-Critical Stochastic Nonlinear Schrödinger Equations with Non-Vanishing Boundary Condition

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Keywords

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