Scattering for critical radial Neumann waves outside a ball

Thomas Duyckaerts; David Lafontaine

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arXiv · 2004.08576

Scattering for critical radial Neumann waves outside a ball

Thomas Duyckaerts·David Lafontaine

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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 $\mathbb R^3$.

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Thomas Duyckaerts, David Lafontaine. 2020-04-18. Scattering for critical radial Neumann waves outside a ball. https://arxiv.org/abs/2004.08576

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