Mathematical Research Letters

Volume 19 (2012)

Number 1

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

Pages: 213 – 232

DOI: https://dx.doi.org/10.4310/MRL.2012.v19.n1.a17

Authors

Dong Li (Department of Mathematics, University of British Columbia, Vancouver, BC, Canada V6T 1Z2)

Hart Smith (Department of Mathematics, University of Washington, Seattle, WA 98195-4350, USA)

Xiaoyi Zhang (Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, 52242 USA; Chinese Academy of Science, Beijing, China)

Abstract

We consider the defocusing energy-critical nonlinear Schrödinger (NLS) in the exterior ofthe unit ball in three dimensions. For the initial value problemwith Dirichlet boundary condition, we prove global well-posedness andscattering with large radial initial data in the Sobolev space $\dotH_0^1$. We also point out that the same strategy can be used totreat the energy-supercritical NLS in the exterior of balls withDirichlet boundary condition and radial $\dot H_0^1$ initial data.

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Published 2 May 2012