Scattering for critical radial Neumann waves outside a ball
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 $\mathbb R^3$.
- Publication:
-
arXiv e-prints
- Pub Date:
- April 2020
- DOI:
- 10.48550/arXiv.2004.08576
- arXiv:
- arXiv:2004.08576
- Bibcode:
- 2020arXiv200408576D
- Keywords:
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- Mathematics - Analysis of PDEs;
- 35L70 (Primary) 34B15;
- 34D05 (Secondary)