Advances in Differential Equations

Interaction Morawetz estimate for the magnetic Schrödinger equation and applications

James Colliander, Magdalena Czubak, and Jeonghun J. Lee

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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

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10] 35Q41: Time-dependent Schrödinger equations, Dirac equations

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.


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