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

Abstract

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.

25 pages, to appear in Math. Research Letter

References in corpus (3)

• Global well-posedness and scattering for the defocusing, $L^2$-critical, nonlinear Schr{ö}dinger equation when $d=2$
• Scattering for H^1/2 bounded solutions to the cubic, defocusing NLS in 3 dimensions
• Global well-posedness for the defocusing, cubic, nonlinear Schrodinger equation when n = 3 via a linear-nonlinear decomposition