Mathematical Research Letters
Volume 19 (2012)
Global well-posedness and scattering for defocusing energy-critical NLS in the exterior of balls with radial data
Pages: 213 – 232
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.