Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Well-posedness for the 1D cubic nonlinear Schr\"odinger equation in
  $L^p$, $p>2$   In this paper, local well-posedness is shown for the one dimensional cubic
nonlinear Schr\"odinger equation in $L^p$-spaces for $2<p<4$, which generalizes
a classical result for $p=2$ by Y. Tsutsumi and recent work for $1<p<2$ by Y.
Zhou. As a consequence, a local theory of solutions is established for a class
of data which decay more slowly than square integrable functions. Regularity
properties of the local solutions in the $L^p$-based Sobolev spaces and
Stricharz spaces are also proved.

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The categories of this paper are: q-bio
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
33
The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: eess
4
The categories of this paper are: cond-mat
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The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th
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The categories of this paper are: q-fin
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The categories of this paper are: hep-th
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The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph