Energy Scattering Theory for Electromagnetic NLS in Dimension Two  

作　　者：Jun Yong ZHANG Ji Qiang ZHENG 

机构地区：[1]Department of Mathematics, Beijing Institute of Technology, Beijing 100081, P. R. China Beijing Computational Science Research Center, Beijing 100193, P. R. China [2]Department of Mathematics, Universitd Nice Sophia-Antipolis, 06108 Nice Cedex 02, France

出　　处：《Acta Mathematica Sinica,English Series》2018年第4期641-654,共14页数学学报（英文版）

基　　金：Supported by NSFC(Grant Nos.11771041 and 11401024);ERC-2014-CoG

摘　　要：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.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.

关 键 词：Nonlinear Schrodinger equations Aharonov-Bohm potential global well-posedness scat-tering 

分 类 号：O441[理学—电磁学]