Scattering theory for nonlinear Schrödinger equations with inverse-square potential

Junyong Zhang; Jiqiang Zheng

doi:10.1016/j.jfa.2014.08.012

Scattering theory for nonlinear Schrödinger equations with inverse-square potential

Junyong Zhang^*, Jiqiang Zheng

^*此作品的通讯作者

数学学院

科研成果: 期刊稿件 › 文章 › 同行评审

57 引用（Scopus）

摘要

We study the long-time behavior of solutions to nonlinear Schrödinger equations with some critical rough potential of a|x|^-2 type. The new ingredients are the interaction Morawetz-type inequalities and Sobolev norm property associated with P_a=-δ+a|x|^-2. We use such properties to obtain the scattering theory for the defocusing energy-subcritical nonlinear Schrödinger equation with inverse square potential in energy space H¹(Rn).

源语言	英语
页（从-至）	2907-2932
页数	26
期刊	Journal of Functional Analysis
卷	267
期	8
DOI	https://doi.org/10.1016/j.jfa.2014.08.012
出版状态	已出版 - 15 10月 2014

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title = "Scattering theory for nonlinear Schr{\"o}dinger equations with inverse-square potential",

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

keywords = "Interaction Morawetz estimates, Inverse square potential, Nonlinear Schr{\"o}dinger equation, Scattering",

author = "Junyong Zhang and Jiqiang Zheng",

note = "Publisher Copyright: {\textcopyright} 2014.",

year = "2014",

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

AU - Zhang, Junyong

AU - Zheng, Jiqiang

PY - 2014/10/15

Y1 - 2014/10/15

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

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

KW - Interaction Morawetz estimates

KW - Inverse square potential

KW - Nonlinear Schrödinger equation

KW - Scattering

UR - http://www.scopus.com/inward/record.url?scp=85027926265&partnerID=8YFLogxK

U2 - 10.1016/j.jfa.2014.08.012

DO - 10.1016/j.jfa.2014.08.012

M3 - Article

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VL - 267

SP - 2907

EP - 2932

JO - Journal of Functional Analysis

JF - Journal of Functional Analysis

IS - 8

ER -

Scattering theory for nonlinear Schrödinger equations with inverse-square potential

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