Energy Scattering Theory for Electromagnetic NLS in Dimension Two

We study the well-posedness and long-time behavior of solution to both defocusing and focusing nonlinear Schrodinger 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-t...

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Bibliographic Details
Published in:Acta mathematica Sinica. English series 2018-04, Vol.34 (4), p.641-654
Main Authors: Zhang, Jun Yong, Zheng, Ji Qiang
Format: Article
Language:English
Subjects:
Coulomb potential
Defocusing
Mathematics
Mathematics and Statistics
Nonlinear equations
Scattering
Schrodinger
尺寸
精力
散布
NLS
电磁
相互作用
非线性
Well posed problems
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Summary:We study the well-posedness and long-time behavior of solution to both defocusing and focusing nonlinear Schrodinger 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.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-018-7253-0