Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Global existence for quasilinear wave equations close to Schwarzschild   In this article we study the quasilinear wave equation $\Box_{g(u, t, x)} u =
0$ where the metric $g(u, t, x)$ is close to the Schwarzschild metric. Under
suitable assumptions of the metric coefficients, and assuming that the initial
data for $u$ is small enough, we prove global existence of the solution. The
main technical result of the paper is a local energy estimate for the linear
wave equation on metrics with slow decay to the Schwarzschild metric.

17
The categories of this paper are: q-fin
5
The categories of this paper are: gr-qc
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
26
The categories of this paper are: bayes-an
34
The categories of this paper are: chem-ph
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
6
The categories of this paper are: astro-ph
10
The categories of this paper are: q-bio
18
The categories of this paper are: econ
36
The categories of this paper are: cmp-lg