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

Benjamin Dodson

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arXiv · 0910.2260

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

Benjamin Dodson

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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.

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Benjamin Dodson. 2011-10-14. Global well-posedness for the defocusing, cubic, nonlinear Schrodinger equation when n = 3 via a linear-nonlinear decomposition. https://arxiv.org/abs/0910.2260

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