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arXiv · 2106.16183

On the supercritical Schr\"{o}dinger equation on the exterior of a ball

Piero D'Ancona
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Abstract

We consider the mixed problem on the exterior of the unit ball in $\mathbb{R}^{n}$, $n\ge2$, for a defocusing Schr\"{o}dinger equation with a power nonlinearity $|u|^{p-1}u$, with zero boundary data. Assuming that the initial data are non radial, sufficiently small perturbations of \emph{large} radial initial data, we prove that for all powers $p>n+6$ the solution exists for all times, its Sobolev norms do not inflate, and the solution is unique in the energy class.

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Piero D'Ancona. 2021-06-30. On the supercritical Schr\"{o}dinger equation on the exterior of a ball. https://arxiv.org/abs/2106.16183

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