Interaction Morawetz estimate for the magnetic Schrödinger equation and applications

We establish an interaction Morawetz estimate for the magnetic Schrödinger 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 Schrödinger equation for $n = 3.$

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