  A coupled system of semilinear wave equations is considered, and a small data
global existence result related to the Strauss conjecture is proved. Previous
results have shown that one of the powers may be reduced below the critical
power for the Strauss conjecture provided the other power sufficiently exceeds
such. The stability of such results under asymptotically flat perturbations of
the space-time where an integrated local energy decay estimate is available is
established.
