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arXiv · 1010.0040

Global well-posedness and scattering for the defocusing, $L^{2}$-critical, nonlinear Schr\"odinger equation when $d = 1$

Benjamin Dodson
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Abstract

In this paper we prove that the defocusing, quintic nonlinear Schr\"odinger initial value problem is globally well-posed and scattering for $u_{0} \in L^{2}(\mathbf{R})$. To do this, we will prove a frequency localized interaction Morawetz estimate similar to the estimate made in [11]. Since we are considering an $L^{2}$ - critical initial value problem we will localize to low frequencies.

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Benjamin Dodson. 2010-10-01. Global well-posedness and scattering for the defocusing, $L^{2}$-critical, nonlinear Schr\"odinger equation when $d = 1$. https://arxiv.org/abs/1010.0040

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