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

#### 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 $n=3$.

#### Article information

Source
Adv. Differential Equations Volume 19, Number 9/10 (2014), 805-832.

Dates
First available in Project Euclid: 1 July 2014