  In this paper, we study the long time dynamics of solutions to the defocusing
semilinear wave equation $\Box_g\phi=|\phi|^{p-1}\phi$ on the Schwarzschild
black hole spacetimes. For $\frac{1+\sqrt{17}}{2}<p<5$ and sufficiently smooth
and localized initial data, we show that the solution decays like
$|\phi|\lesssim t^{-1+\epsilon}$ in the domain of outer communication. The
proof relies on the $r$-weighted vector field method of Dafermos-Rodnianski
together with the Strichartz estimates for linear waves by
Marzuola-Metcalfe-Tataru-Tohaneanu.
