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

^*Corresponding author for this work

School of Mathematics and Statistics

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

2 Citations (Scopus)

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.

Original language	English
Pages (from-to)	641-654
Number of pages	14
Journal	Acta Mathematica Sinica, English Series
Volume	34
Issue number	4
DOIs	https://doi.org/10.1007/s10114-018-7253-0
Publication status	Published - 1 Apr 2018

Keywords

Aharonov–Bohm potential
Nonlinear Schrödinger equations
global well-posedness
scattering

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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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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

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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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