  We explore the global existence of solutions to systems of quasilinear wave
equations satisfying the null condition when the initial data are sufficiently
small. We adapt an approach of Keel, Smith, and Sogge, which relies on
integrated local energy estimates and a weighted Sobolev estimate that yields
decay in $|x|$, by using the $r^p$-weighted local energy estimates of Dafermos
and Rodnianski. One advantage of this approach is that all time-dependent
vector fields can be avoided and the proof can be readily adapted to address
wave equations exterior to star-shaped obstacles.
