Global well-posedness and scattering for defocusing energy-critical NLS in the exterior of balls with radial data

Dong Li; Hart Smith; Xiaoyi Zhang

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arXiv · 1109.4194

Global well-posedness and scattering for defocusing energy-critical NLS in the exterior of balls with radial data

Dong Li·Hart Smith·Xiaoyi Zhang

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Abstract

We consider the defocusing energy-critical NLS in the exterior of the unit ball in three dimensions. For the initial value problem with Dirichlet boundary condition we prove global well-posedness and scattering with large radial initial data in the Sobolev space $\dot H_0^1$. We also point out that the same strategy can be used to treat the energy-supercritical NLS in the exterior of balls with Dirichlet boundary condition and radial $\dot H_0^1$ initial data.

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Dong Li, Hart Smith, Xiaoyi Zhang. 2011-09-20. Global well-posedness and scattering for defocusing energy-critical NLS in the exterior of balls with radial data. https://arxiv.org/abs/1109.4194

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