On the supercritical defocusing NLW outside a ball

Abstract

We study a defocusing semilinear wave equation, with a power nonlinearity $|u{|}^{p-1}u$, defined outside the unit ball of ${\mathbb{R}}^n$, $n\ge 3$, with Dirichlet boundary conditions. We prove that if $p>n+4$ 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 pointwise decay estimate for the exterior linear wave equation perturbed with a large, time dependent potential.

20 pages

Cited by in corpus (1)

• On the supercritical Schrödinger equation on the exterior of a ball