## Advances in Differential Equations

### 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

Permanent link to this document
https://projecteuclid.org/euclid.ade/1404230124

Mathematical Reviews number (MathSciNet)
MR3229599

Zentralblatt MATH identifier
1296.35167

#### Citation

Colliander, James; Czubak, Magdalena; Lee, Jeonghun J. Interaction Morawetz estimate for the magnetic Schrödinger equation and applications. Adv. Differential Equations 19 (2014), no. 9/10, 805--832. https://projecteuclid.org/euclid.ade/1404230124