  We consider the wave equation (-\dt^2+\dr^2 -V -V_L(-\Delta_{S^2})) u =
fF'(|u| ^2) u with (t,\rho,\theta,\phi) in R x R x S^2. The wave equation on a
spherically symmetric manifold with a single closed geodesic surface or on the
exterior of the Schwarzschild manifold can be reduced to this form. Using a
smoothed Morawetz estimate which does not require a spherical harmonic
decomposition, we show that there is decay in L^2_{loc} for initial data in the
energy class, even if the initial data is large. This requires certain
conditions on the potentials V, V_L, and f. We show that a key condition on the
weight in the smoothed Morawetz estimate can be reduced to an ODE condition,
which is verified numerically.
