Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Local well-posedness of the KdV equation with quasi periodic initial
  data   We prove the local well-posedness for the Cauchy problem of the Korteweg-de
Vries equation in a quasi periodic function space. The function space contains
functions such that f=f_1+f_2+...+f_N where f_j is in the Sobolev space of
order s>-1/2N of a_j periodic functions. Note that f is not a periodic function
when the ratio of periods a_i/a_j is irrational. The main tool of the proof is
the Fourier restriction norm method introduced by Bourgain. We also prove an
ill-posedness result in the sense that the flow map (if it exists) is not C^2,
which is related to the Diophantine problem.

13
The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
27
The categories of this paper are: comp-gas
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
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The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con