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

School of Mathematical & Computer Sciences

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

2 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 - 15 Dec 2022

Keywords

Geometry and Topology
Algebra and Number Theory
Analysis

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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 = "Geometry and Topology, Algebra and Number Theory, Analysis",

author = "Kelvin Cheung and Guopeng Li",

year = "2022",

month = dec,

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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 - 2022/12/15

Y1 - 2022/12/15

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 - Geometry and Topology

KW - Algebra and Number Theory

KW - Analysis

U2 - 10.1619/fesi.65.287

DO - 10.1619/fesi.65.287

M3 - Article

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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