Global well-posedness and scattering for the defocusing, cubic nonlinear Schrödinger equation when $n = 3$ via a linear-nonlinear decomposition

Benjamin Dodson

doi:10.3934/dcds.2013.33.1905

Article Contents

2013, Volume 33, Issue 5: 1905-1926. Doi: 10.3934/dcds.2013.33.1905

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Global well-posedness and scattering for the defocusing, cubic nonlinear Schrödinger equation when $n = 3$ via a linear-nonlinear decomposition

Benjamin Dodson^1,

1.
970 Evans Hall, number 3840, UC Berkeley mathematics, Berkeley, CA 94720-3840

Received: October 2011

Revised: September 2012

Published: May 2013

Abstract / Introduction Related Papers Cited by

Abstract

In this paper, we prove global well-posedness and scattering for the defocusing, cubic nonlinear Schrödinger equation when $n = 3$ and $u_{0} \in H^{s}(\mathbf{R}^{3})$, $s > 5/7$. To this end, we utilize a linear-nonlinear decomposition, similar to the decomposition used in [20] for the wave equation.

Keywords:

Nonlinear Schrödinger equation.

Mathematics Subject Classification: Primary: 35Q55.

Citation:

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