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

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

2009-10-12

arxiv.org/abs/0910.2260v2

Mathematics

Analysis of PDEs

26 pages

Scientific paper

In this paper, we prove global well-posedness and scattering for the
defocusing, cubic nonlinear Schr{\"o}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.

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