We study the semilinear wave equation
\[
∂
t
2
ψ
−
Δ
ψ
=
|
ψ
|
p
−
1
ψ
\partial _t^2 \psi -\Delta \psi =|\psi |^{p-1}\psi
\]
for
p
>
3
p > 3
with radial data in three spatial dimensions. There exists an explicit solution which blows up at
t
=
T
>
0
t=T>0
given by
\[
ψ
T
(
t
,
x
)
=
c
p
(
T
−
t
)
−
2
p
−
1
,
\psi ^T(t,x)=c_p (T-t)^{-\frac {2}{p-1}},
\]
where
c
p
c_p
is a suitable constant. We prove that the blow up described by
ψ
T
\psi ^T
is stable in the sense that there exists an open set (in a topology strictly stronger than the energy) of radial initial data that leads to a solution which converges to
ψ
T
\psi ^T
as
t
→
T
−
t\to T-
in the backward lightcone of the blow up point
(
t
,
r
)
=
(
T
,
0
)
(t,r)=(T,0)
.