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

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

2011-11-17

arxiv.org/abs/1111.4021v3

Mathematics

Analysis of PDEs

25 pages, to appear in Math. Research Letter

Scientific paper

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

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