Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Almost sure well-posedness of the cubic nonlinear Schr\"odinger equation
  below L^2(T)   We consider the Cauchy problem for the one-dimensional periodic cubic
nonlinear Schr\"odinger equation (NLS) with initial data below L^2. In
particular, we exhibit nonlinear smoothing when the initial data are
randomized. Then, we prove local well-posedness of NLS almost surely for the
initial data in the support of the canonical Gaussian measures on H^s(T) for
each s > -1/3, and global well-posedness for each s > -1/12.

22
The categories of this paper are: chao-dyn
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
11
The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph