Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global well-posedness for the defocusing, quintic nonlinear
  Schr\"odinger equation in one dimension   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.

9
The categories of this paper are: nlin
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
29
The categories of this paper are: funct-an
19
The categories of this paper are: eess
8
The categories of this paper are: hep-ex
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
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The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
4
The categories of this paper are: cond-mat