Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global well-posedness and scattering for the defocusing,
  $L^{2}$-critical, nonlinear Schr{\"o}dinger equation when $d = 2$   In this paper we prove that the defocusing, cubic nonlinear Schr{\"o}dinger
initial value problem is globally well-posed and scattering for $u_{0} \in
L^{2}(\mathbf{R}^{2})$. To do this, we will prove a frequency localized
interaction Morawetz estimate similar to the estimate made in \cite{CKSTT4}.
Since we are considering an $L^{2}$ - critical initial value problem we will
localize to low frequencies.

23
The categories of this paper are: solv-int
10
The categories of this paper are: q-bio
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ