@article{24be9c46c79045b280385db00c29c5d7,
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.",
year = "2018",
month = apr,
day = "1",
doi = "10.1007/s10114-018-7253-0",
language = "English",
volume = "34",
pages = "641--654",
journal = "Acta Mathematica Sinica, English Series",
issn = "1439-8516",
publisher = "Springer Verlag",
number = "4",
}