Global well-posedness for the defocusing, cubic, nonlinear Schrodinger equation when n = 3 via a linear-nonlinear decomposition

Abstract

In this paper, we prove global well-posedness and scattering for the defocusing, cubic nonlinear Schr{ö}dinger equation in three dimensions when $n=3$ when $u_0\in H^s({\mathbf{R}}^3)$, $s>3/4$. To this end, we utilize a linear-nonlinear decomposition, similar to the decomposition used in [12] for the wave equation.

26 pages