Scattering theory for nonlinear Schrodinger equations with inverse-square potential

Junyong Zhang; Jiqiang Zheng

doi:10.1016/j.jfa.2014.08.012

Scattering theory for nonlinear Schrodinger equations with inverse-square potential

Junyong Zhang, Jiqiang Zheng

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

Abstract

We study the long-time behavior of solutions to nonlinear SchrÃ¶dinger equations with some critical rough potential of a|x| âˆ’2 type. The new ingredients are the interaction Morawetz-type inequalities and Sobolev norm property associated with Pa = âˆ’Î” + a|x|âˆ’2. We use such properties to obtain the scattering theory for the defocusing energysubcritical nonlinear SchrÃ¶dinger equation with inverse square potential in energy space H1(Rn).

Original language	English
Pages (from-to)	2907-2932
Journal	Journal of Functional Analysis
Volume	267
Issue number	8
DOIs	https://doi.org/10.1016/j.jfa.2014.08.012
Publication status	Published - 2014

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10.1016/j.jfa.2014.08.012

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@article{14b7bfa24740481b97b59fda40536774,

title = "Scattering theory for nonlinear Schrodinger equations with inverse-square potential",

abstract = "We study the long-time behavior of solutions to nonlinear Schr{\~A}¶dinger equations with some critical rough potential of a|x| {\^a}ˆ{\textquoteright}2 type. The new ingredients are the interaction Morawetz-type inequalities and Sobolev norm property associated with Pa = {\^a}ˆ{\textquoteright}{\^I}” + a|x|{\^a}ˆ{\textquoteright}2. We use such properties to obtain the scattering theory for the defocusing energysubcritical nonlinear Schr{\~A}¶dinger equation with inverse square potential in energy space H1(Rn).",

author = "Junyong Zhang and Jiqiang Zheng",

year = "2014",

doi = "10.1016/j.jfa.2014.08.012",

language = "English",

volume = "267",

pages = "2907--2932",

journal = "Journal of Functional Analysis",

publisher = "Academic Press",

number = "8",

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TY - JOUR

T1 - Scattering theory for nonlinear Schrodinger equations with inverse-square potential

AU - Zhang, Junyong

AU - Zheng, Jiqiang

PY - 2014

Y1 - 2014

N2 - We study the long-time behavior of solutions to nonlinear SchrÃ¶dinger equations with some critical rough potential of a|x| âˆ’2 type. The new ingredients are the interaction Morawetz-type inequalities and Sobolev norm property associated with Pa = âˆ’Î” + a|x|âˆ’2. We use such properties to obtain the scattering theory for the defocusing energysubcritical nonlinear SchrÃ¶dinger equation with inverse square potential in energy space H1(Rn).

AB - We study the long-time behavior of solutions to nonlinear SchrÃ¶dinger equations with some critical rough potential of a|x| âˆ’2 type. The new ingredients are the interaction Morawetz-type inequalities and Sobolev norm property associated with Pa = âˆ’Î” + a|x|âˆ’2. We use such properties to obtain the scattering theory for the defocusing energysubcritical nonlinear SchrÃ¶dinger equation with inverse square potential in energy space H1(Rn).

U2 - 10.1016/j.jfa.2014.08.012

DO - 10.1016/j.jfa.2014.08.012

M3 - Article

VL - 267

SP - 2907

EP - 2932

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 8

ER -

Scattering theory for nonlinear Schrodinger equations with inverse-square potential

Abstract

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