Mathematical Research Letters

Volume 19 (2012)

Number 2

Global well–posedness and scattering for the defocusing, cubic NLS in $\mathbb{R}^3$

Pages: 431 – 451

DOI: http://dx.doi.org/10.4310/MRL.2012.v19.n2.a14

Author

Qingtang Su (Department of Mathematics and Statistics, Auburn University, Auburn 36849, AL, U.S.A.)

Abstract

We prove global well-posedness and scattering for the defocusing, cubic NLS on $\mathbb{R}^3$ withinitial data in $H^s(\mathbb{R}^3)$ for $s>49/74$. The proof combines the ideas of resonancedecomposition in \cite{CKSTT4} and linear–nonlinear decomposition in \cite{ben1,roy} togetherwith the idea of large time iteration.

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