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Global well-posedness and scattering for defocusing, cubic NLS in $\mathbb{R}^3$ (1111.4021v3)
Published 17 Nov 2011 in math.AP
Abstract: We prove global well-posedness and scattering for the defocusing, cubic NLS on $\mathbb{R}3$ with initial data in $Hs(\mathbb{R}3)$ 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.