Global well-posedness of the Gross-Pitaevskii and cubic-quintic nonlinear Schrödinger equations with non-vanishing boundary conditions

Rowan Killip; Tadahiro Oh; Oana Pocovnicu; Monica Visan

doi:10.4310/MRL.2012.v19.n5.a1

Global well-posedness of the Gross-Pitaevskii and cubic-quintic nonlinear Schrödinger equations with non-vanishing boundary conditions

Rowan Killip^*, Tadahiro Oh, Oana Pocovnicu, Monica Visan

^*Corresponding author for this work

School of Mathematics

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

Abstract

We consider the Gross-Pitaevskii equation on R^4 and the cubic-quintic nonlinear Schrodinger equation (NLS) on R^3 with non-vanishing boundary conditions at spatial infinity. By viewing these equations as perturbations to the energy-critical NLS, we prove that they are globally well-posed in their energy spaces. In particular, we prove unconditional uniqueness in the energy spaces for these equations.

Original language	English
Pages (from-to)	969-986
Number of pages	18
Journal	Mathematical research letters
Volume	19
Issue number	5
DOIs	https://doi.org/10.4310/MRL.2012.v19.n5.a1
Publication status	Published - 2012

Keywords / Materials (for Non-textual outputs)

NLS
Gross–Pitaevskii equation
non-vanishing boundary condition

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Global well-posedness of the Gross-Pitaevskii and cubic-quintic nonlinear Schrödinger equations with non-vanishing boundary conditionsAccepted author manuscript, 197 KB

http://intlpress.com/site/pub/pages/journals/items/mrl/content/vols/0019/0005/a001/index.html

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title = "Global well-posedness of the Gross-Pitaevskii and cubic-quintic nonlinear Schr{\"o}dinger equations with non-vanishing boundary conditions",

abstract = "We consider the Gross-Pitaevskii equation on R\textasciicircum{}4 and the cubic-quintic nonlinear Schrodinger equation (NLS) on R\textasciicircum{}3 with non-vanishing boundary conditions at spatial infinity. By viewing these equations as perturbations to the energy-critical NLS, we prove that they are globally well-posed in their energy spaces. In particular, we prove unconditional uniqueness in the energy spaces for these equations.",

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author = "Rowan Killip and Tadahiro Oh and Oana Pocovnicu and Monica Visan",

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language = "English",

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pages = "969--986",

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T1 - Global well-posedness of the Gross-Pitaevskii and cubic-quintic nonlinear Schrödinger equations with non-vanishing boundary conditions

AU - Killip, Rowan

AU - Oh, Tadahiro

AU - Pocovnicu, Oana

AU - Visan, Monica

PY - 2012

Y1 - 2012

N2 - We consider the Gross-Pitaevskii equation on R^4 and the cubic-quintic nonlinear Schrodinger equation (NLS) on R^3 with non-vanishing boundary conditions at spatial infinity. By viewing these equations as perturbations to the energy-critical NLS, we prove that they are globally well-posed in their energy spaces. In particular, we prove unconditional uniqueness in the energy spaces for these equations.

AB - We consider the Gross-Pitaevskii equation on R^4 and the cubic-quintic nonlinear Schrodinger equation (NLS) on R^3 with non-vanishing boundary conditions at spatial infinity. By viewing these equations as perturbations to the energy-critical NLS, we prove that they are globally well-posed in their energy spaces. In particular, we prove unconditional uniqueness in the energy spaces for these equations.

KW - NLS

KW - Gross–Pitaevskii equation

KW - non-vanishing boundary condition

U2 - 10.4310/MRL.2012.v19.n5.a1

DO - 10.4310/MRL.2012.v19.n5.a1

M3 - Article

SN - 1073-2780

VL - 19

SP - 969

EP - 986

JO - Mathematical research letters

JF - Mathematical research letters

IS - 5

ER -

Global well-posedness of the Gross-Pitaevskii and cubic-quintic nonlinear Schrödinger equations with non-vanishing boundary conditions

Abstract

Keywords / Materials (for Non-textual outputs)

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