Interaction Morawetz estimate for the magnetic Schrödinger equation and applications

Details Interaction Morawetz estimate for the magnetic Schrödinger equation and applications Interaction Morawetz estimate for the magnetic Schrödinger equation and applications

2011-12-19

arxiv.org/abs/1112.4452v1

Mathematics

Analysis of PDEs

23 pages; Submitted

Scientific paper

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

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