Energy Scattering Theory for Electromagnetic NLS in Dimension Two

Jun Yong Zhang; Ji Qiang Zheng

doi:10.1007/s10114-018-7253-0

Energy Scattering Theory for Electromagnetic NLS in Dimension Two

Jun Yong Zhang^*, Ji Qiang 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

2 引用（Scopus）

摘要

We study the well-posedness and long-time behavior of solution to both defocusing and focusing nonlinear Schr¨odinger equations with scaling critical magnetic potentials in dimension two. In the defocusing case, and under the assumption that the initial data is radial, we prove interaction Morawetz-type inequalities and show the scattering holds in the energy space. The magnetic potential considered here is the Aharonov–Bohm potential which decays likely the Coulomb potential |x|⁻¹.

源语言	英语
页（从-至）	641-654
页数	14
期刊	Acta Mathematica Sinica, English Series
卷	34
期	4
DOI	https://doi.org/10.1007/s10114-018-7253-0
出版状态	已出版 - 1 4月 2018

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Zhang, J. Y., & Zheng, J. Q. (2018). Energy Scattering Theory for Electromagnetic NLS in Dimension Two. Acta Mathematica Sinica, English Series, 34(4), 641-654. https://doi.org/10.1007/s10114-018-7253-0

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title = "Energy Scattering Theory for Electromagnetic NLS in Dimension Two",

abstract = "We study the well-posedness and long-time behavior of solution to both defocusing and focusing nonlinear Schr¨odinger equations with scaling critical magnetic potentials in dimension two. In the defocusing case, and under the assumption that the initial data is radial, we prove interaction Morawetz-type inequalities and show the scattering holds in the energy space. The magnetic potential considered here is the Aharonov–Bohm potential which decays likely the Coulomb potential |x|−1.",

keywords = "Aharonov–Bohm potential, Nonlinear Schr{\"o}dinger equations, global well-posedness, scattering",

author = "Zhang, {Jun Yong} and Zheng, {Ji Qiang}",

note = "Publisher Copyright: {\textcopyright} 2018, Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature.",

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doi = "10.1007/s10114-018-7253-0",

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TY - JOUR

T1 - Energy Scattering Theory for Electromagnetic NLS in Dimension Two

AU - Zhang, Jun Yong

AU - Zheng, Ji Qiang

N1 - Publisher Copyright: © 2018, Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag GmbH Germany, part of Springer Nature.

PY - 2018/4/1

Y1 - 2018/4/1

N2 - We study the well-posedness and long-time behavior of solution to both defocusing and focusing nonlinear Schr¨odinger equations with scaling critical magnetic potentials in dimension two. In the defocusing case, and under the assumption that the initial data is radial, we prove interaction Morawetz-type inequalities and show the scattering holds in the energy space. The magnetic potential considered here is the Aharonov–Bohm potential which decays likely the Coulomb potential |x|−1.

AB - We study the well-posedness and long-time behavior of solution to both defocusing and focusing nonlinear Schr¨odinger equations with scaling critical magnetic potentials in dimension two. In the defocusing case, and under the assumption that the initial data is radial, we prove interaction Morawetz-type inequalities and show the scattering holds in the energy space. The magnetic potential considered here is the Aharonov–Bohm potential which decays likely the Coulomb potential |x|−1.

KW - Aharonov–Bohm potential

KW - Nonlinear Schrödinger equations

KW - global well-posedness

KW - scattering

UR - http://www.scopus.com/inward/record.url?scp=85043755447&partnerID=8YFLogxK

U2 - 10.1007/s10114-018-7253-0

DO - 10.1007/s10114-018-7253-0

M3 - Article

AN - SCOPUS:85043755447

SN - 1439-8516

VL - 34

SP - 641

EP - 654

JO - Acta Mathematica Sinica, English Series

JF - Acta Mathematica Sinica, English Series

IS - 4

ER -

Energy Scattering Theory for Electromagnetic NLS in Dimension Two

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