Scattering for critical radial Neumann waves outside a ball

• Thomas Duyckaerts ^[2] ; David Lafontaine ^[1]
  1. [1] University of Bath

     University of Bath

     Reino Unido

     
  2. [2] Université Sorbonne Paris Nord, Villetaneuse
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 38, Nº 2, 2022, págs. 659-703
• Idioma: inglés
• DOI: 10.4171/RMI/1290
• Texto completo no disponible (Saber más ...)
• Resumen

  • 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.