On the supercritical defocusing NLW outside a ball

2019/12/31 by D'Ancona, Piero
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1912.13216

Abstract

We study a defocusing semilinear wave equation, with a power nonlinearity |u|^p-1u, defined outside the unit ball of ℝⁿ, n≥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.

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