Global well-posedness and scattering for the defocusing, L2-critical, nonlinear Schrödinger equation when d=2

Benjamin Dodson

Type: Article

Publication Date: 2016-09-12

Citations: 172

DOI: https://doi.org/10.1215/00127094-3673888

Abstract

In this article we prove that the defocusing, cubic nonlinear Schrödinger initial value problem is globally well posed and scattering for u0∈L2(R2). The proof uses the bilinear estimates of Planchon and Vega and a frequency-localized interaction Morawetz estimate similar to the high-frequency estimate of Colliander, Keel, Staffilani, Takaoka, and Tao and especially the low-frequency estimate of Dodson.

Locations

Duke Mathematical Journal - View
arXiv (Cornell University) - View - PDF
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