Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global existence for Dirichlet-wave equations with quadratic
  nonlinearties in high dimensions   We prove global existence of solutions to quasilinear wave equations with
quadratic nonlinearities exterior to nontrapping obstacles in spatial
dimensions four and higher. This generalizes a result of Shibata and Tsutsumi
in spatial dimensions greater than or equal to six. The technique of proof
would allow for more complicated geometries provided that an appropriate local
energy decay exists for the associated linear wave equation.

19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
12
The categories of this paper are: nucl-th
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex