  In \cite{Luk}, Luk proved global existence for semilinear wave equations in
Kerr spacetime with small angular momentum($a\ll M$) \[
\Box_{g_K}\phi=F(\partial \phi), \] when the quadratic nonlinear term satisfies
the null condition. In this work, we will show that if the null condition does
not hold, at most we can have almost global existence for semilinear wave
equations with quadratic nonlinear term in Schwarzschild spacetime, which is
the special case of Kerr with $a=0$ \[ \Box_{g_S}\phi=(\partial_t\phi)^2, \]
where $\Box_{g_S}$ denotes the D'Alembert operator associated with
Schwarzschild metric. What is more, if the power of the nonlinear term is
replaced with $p$ satisfying $3/2\le p< 2$, we still can show blow-up, no
matter how small the initial data are. We do not have to assume that the
support of the data should be far away from the event horizon.
