AbstractWe study a defocusing semilinear wave equation, with a power nonlinearity $$|u|^{p-1}u$$
|
u
|
p
-
1
u
, defined outside the unit ball of $$\mathbb {R}^{n}$$
R
n
, $$n\ge 3$$
n
≥
3
, with Dirichlet boundary conditions. We prove that if $$p>n+3$$
p
>
n
+
3
and the initial data are nonradial perturbations of large radial data, there exists a global smooth solution. The solution is unique among energy class solutions satisfying an energy inequality. The main tools used are the Penrose transform and a Strichartz estimate for the exterior linear wave equation perturbed with a large, time dependent potential.
Fractal Strichartz estimate for the wave equation
