Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global dynamics below the ground state for the quadratic Sch\"odinger
  system in 5d   In this paper we consider the nonlinear Schr\"odinger system (NLS) with
quadratic interaction in five dimensions. We determine the global behavior of
the solutions to the system with data below the ground state. Our proof of the
scattering result is based on an argument by Kenig Merle [16]. In particular,
the new part of this paper is to deal with asymmetric interaction. A blowing up
or growing up result is proved by combining the argument by Du Wu Zhang in [6]
and a variational characterization of minimizers. Moreover, we show a
blowing-up result if the data has finite variance or is radial.

1
The categories of this paper are: cs
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
34
The categories of this paper are: chem-ph
30
The categories of this paper are: q-alg
33
The categories of this paper are: plasm-ph
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
26
The categories of this paper are: bayes-an
27
The categories of this paper are: comp-gas