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

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

2009-10-20

arxiv.org/abs/0910.3964v1

Mathematics

Analysis of PDEs

25 pages

Scientific paper

In this paper, we prove global well-posedness for low regularity data for the one dimensional quintic defocusing nonlinear Schr\"odinger 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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