Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solutions globales pour l'\'equation de Schr\"odinger cubique en
  dimension 3   The purpose of this article is to construct global solutions for some
super-crtical Schrodinger equations using the theory of random data introduced
by N.Burq and N.Tzvetkov. We begin our study by the cubic equation in three
dimension. Thanks to the lens transform, it suffices to study a local theory
for the Schr\"odinger equations with harmonic potential and we can establish
Bourgain type bilinear estimates for the harmonic oscillator. Then, we explain
how we can generalize this result in all dimensions.

18
The categories of this paper are: econ
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
14
The categories of this paper are: math-ph
10
The categories of this paper are: q-bio
16
The categories of this paper are: stat
34
The categories of this paper are: chem-ph
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat