Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global existence for solutions of the focusing wave equation with the
  compactness property   We prove that every solution of the focusing energy-critical wave equation
with the compactness property is global. We also give similar results for
supercritical wave and Schr\"odinger equations.

11
The categories of this paper are: hep-lat
8
The categories of this paper are: hep-ex
30
The categories of this paper are: q-alg
32
The categories of this paper are: atom-ph
19
The categories of this paper are: eess
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
26
The categories of this paper are: bayes-an
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
15
The categories of this paper are: nucl-ex
3
The categories of this paper are: physics