James Colliander, Magdalena Czubak, Jeonghun Lee
Published 2011-12-19, updated 2014-04-16Version 2
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 $n = 3.$
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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