Abstract
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 $n=3$.
Citation
James Colliander. Magdalena Czubak. Jeonghun J. Lee. "Interaction Morawetz estimate for the magnetic Schrödinger equation and applications." Adv. Differential Equations 19 (9/10) 805 - 832, September/October 2014. https://doi.org/10.57262/ade/1404230124
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