Interaction Morawetz estimate for the magnetic Schr\"odinger equation and applications

James Colliander; Magdalena Czubak; Jeonghun Lee

Interaction Morawetz estimate for the magnetic Schr\"odinger equation and applications

Analysis of PDEs 2014-04-17 v2

Authors: James Colliander , Magdalena Czubak , Jeonghun Lee

Abstract

We establish an interaction Morawetz estimate for the magnetic Schr\"odinger equation for $n\geq 3$ under certain smallness conditions on the gauge potentials, but with almost optimal decay. As an application, we prove global wellposedness and scattering in $H^1$ for the cubic defocusing magnetic Schr\"odinger equation for $n = 3.$

Keywords

interaction Morawetz estimate magnetic Schrödinger equation global wellposedness scattering gauge potential

Cite

@article{arxiv.1112.4452,
  title  = {Interaction Morawetz estimate for the magnetic Schr\"odinger equation and applications},
  author = {James Colliander and Magdalena Czubak and Jeonghun Lee},
  journal= {arXiv preprint arXiv:1112.4452},
  year   = {2014}
}

Comments

23 pages; Added some remarks in the introduction and more details in the proof of LWP and GWP, fixed typos. To appear in DIE

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