Interaction Morawetz estimate for the magnetic Schr\"odinger equation and applications
Abstract
We establish an interaction Morawetz estimate for the magnetic Schr\"odinger equation for n≥ 3 under certain smallness conditions on the gauge potentials, but with almost optimal decay. As an application, we prove global wellposedness and scattering in H1 for the cubic defocusing magnetic Schr\"odinger equation for n = 3.
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