Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global existence for semilinear wave equations exterior to nontrapping
  obstacles   In this paper, we show global existence, in spatial dimensions greater than
or equal to four, for semilinear wave equations with quadratic nonlinearities
exterior to a nontrapping obstacle. This extends the previous work of
Shibata-Tsutsumi and Hayashi. Shibata-Tsutsumi showed the result for spatial
dimensions greater than or equal to 6, and Hayashi proved the result exterior
to a ball.

22
The categories of this paper are: chao-dyn
7
The categories of this paper are: hep-th
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
35
The categories of this paper are: mtrl-th