Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Resonant decompositions and the I-method for cubic nonlinear Schrodinger
  on R^2   The initial value problem for the cubic defocusing nonlinear Schr\"odinger
equation $i \partial_t u + \Delta u = |u|^2 u$ on the plane is shown to be
globally well-posed for initial data in $H^s (\R^2)$ provided $s>1/2$. The
proof relies upon an almost conserved quantity constructed using multilinear
correction terms. The main new difficulty is to control the contribution of
resonant interactions to these correction terms. The resonant interactions are
significant due to the multidimensional setting of the problem and some
orthogonality issues which arise.

12
The categories of this paper are: nucl-th
18
The categories of this paper are: econ
30
The categories of this paper are: q-alg
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
24
The categories of this paper are: dg-ga
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
7
The categories of this paper are: hep-th
9
The categories of this paper are: nlin