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

Abstract

We consider the defocusing energy-critical nonlinear Schrödinger (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 H 10. 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 H10 initial data. © International Press 2012.