## Duke Mathematical Journal

### Global well-posedness and scattering for the defocusing, $L^{2}$-critical, nonlinear Schrödinger equation when $d=2$

Benjamin Dodson

#### Abstract

In this article we prove that the defocusing, cubic nonlinear Schrödinger initial value problem is globally well posed and scattering for $u_{0}\in L^{2}(\mathbf{R}^{2})$. 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.

#### Article information

Source
Duke Math. J., Volume 165, Number 18 (2016), 3435-3516.

Dates
Revised: 31 January 2016
First available in Project Euclid: 12 September 2016

https://projecteuclid.org/euclid.dmj/1473686054

Digital Object Identifier
doi:10.1215/00127094-3673888

Mathematical Reviews number (MathSciNet)
MR3577369

Zentralblatt MATH identifier
1361.35164

#### Citation

Dodson, Benjamin. Global well-posedness and scattering for the defocusing, $L^{2}$ -critical, nonlinear Schrödinger equation when $d=2$. Duke Math. J. 165 (2016), no. 18, 3435--3516. doi:10.1215/00127094-3673888. https://projecteuclid.org/euclid.dmj/1473686054

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