Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dynamics of the focusing 3D cubic NLS with slowly decaying potential   In this paper, we consider a 3d cubic focusing nonlinear Schr\"odinger
equation (NLS) with slowing decaying potentials. Adopting the variational
method of Ibrahim-Masmoudi-Nakanishi \cite{IMN}, we obtain a condition for
scattering. It is actually sharp in some sense since the solution will blow up
if it's false. The proof of blow-up part relies on the method of Du-Wu-Zhang
\cite{DWZ}

8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex
0
The categories of this paper are: hep-ph
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
21
The categories of this paper are: adap-org
31
The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
30
The categories of this paper are: q-alg