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+ 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.
On the supercritical defocusing NLW outside a ball / D'Ancona, P.. - In: ANALYSIS AND MATHEMATICAL PHYSICS. - ISSN 1664-2368. - 11:4(2021). [10.1007/s13324-021-00576-3]
On the supercritical defocusing NLW outside a ball
D'Ancona P.
2021
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+ 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.File | Dimensione | Formato | |
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