Global well-posedness for the defocusing, quintic nonlinear Schrödinger equation in one dimension

Benjamin Dodson

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arXiv · 0910.3964

Global well-posedness for the defocusing, quintic nonlinear Schrödinger equation in one dimension

Benjamin Dodson

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Abstract

In this paper, we prove global well-posedness for low regularity data for the one dimensional quintic defocusing nonlinear Schrödinger equation. We show that a unique solution exists for $u_{0} \in H^{s}(\mathbf{R})$, $s > {8/29}$. This improves the result in [13], which proved global well-posedness for $s > {1/3}$. The main new argument is that we obtain almost Morawetz estimates with improved error.

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Benjamin Dodson. 2009-10-20. Global well-posedness for the defocusing, quintic nonlinear Schrödinger equation in one dimension. https://arxiv.org/abs/0910.3964

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