  We develop a new method for addressing certain weakly null systems of wave
equations. This approach does not rely on Lorentz invariance nor on the use of
null foliations, both of which restrict applications to, e.g., multiple speed
systems. The proof uses a class of space-time Klainerman-Sobolev estimates of
the first author, Tataru, and Tohaneanu, which pair nicely with local energy
estimates that combine the $r^{p}$-weighted method of Dafermos and Rodnianski
with the ghost weight method of Alinhac. We further refine the standard local
energy estimate with a modification of the $\partial_{t} - \partial_{r}$
portion of the multiplier.
