Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global existence and scattering for rough solutions of a nonlinear
  Schroedinger equation on R^3   We prove global existence and scattering for the defocusing, cubic nonlinear
Schr\"odinger equation in $H^s(\rr^3)$ for $s > {4/5}$. The main new estimate
in the argument is a Morawetz-type inequality for the solution $\phi$. This
estimate bounds $\|\phi(x,t)\|_{L^4_{x,t}(\rr^3 \times \rr)}$, whereas the
well-known Morawetz-type estimate of Lin-Strauss controls
$\int_0^{\infty}\int_{\rr^3}\frac{(\phi(x,t))^4}{|x|} dx dt

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The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
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The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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The categories of this paper are: solv-int
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The categories of this paper are: q-fin
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The categories of this paper are: funct-an
6
The categories of this paper are: astro-ph
14
The categories of this paper are: math-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex