Scattering for critical radial Neumann waves outside a ball

  • Thomas Duyckaerts

    Université Sorbonne Paris Nord, Villetaneuse, France
  • David Lafontaine

    University of Bath, UK
Scattering for critical radial Neumann waves outside a ball cover
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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 .

Cite this article

Thomas Duyckaerts, David Lafontaine, Scattering for critical radial Neumann waves outside a ball. Rev. Mat. Iberoam. 38 (2022), no. 2, pp. 659–703

DOI 10.4171/RMI/1290