Scattering for critical radial Neumann waves outside a ball

Thomas Duyckaerts, David Lafontaine

Research output: Contribution to journalArticlepeer-review

Abstract

We show that the solutions of the three-dimensional critical defocusing nonlinear wave equation with Neumann boundary conditions outside a ball and radial initial data scatter. This is to our knowledge the first result of scattering for a nonlinear wave equation with Neumann boundary conditions. Our proof uses the scheme of concentration-compactness/rigidity introduced by Kenig and Merle, extending it to our setup, together with the so-called channels of energy method to rule out compact-flow solutions. We also obtain, for the focusing equation, the same exact scattering/blow-up dichotomy below the energy of the ground-state as in R3.

Original languageEnglish
Pages (from-to)659-703
Number of pages45
JournalRevista Matematica Iberoamericana
Volume38
Issue number2
Early online date2 Aug 2021
DOIs
Publication statusPublished - 31 Dec 2022

Keywords

  • exterior domain
  • Neumann boundary condition
  • scattering
  • Wave equation

ASJC Scopus subject areas

  • Mathematics(all)

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