Quintic NLS in the exterior of a strictly convex obstacle
  We consider the defocusing energy-critical nonlinear Schr\"odinger equation in the exterior of a smooth compact strictly convex obstacle in three dimensions. For the initial-value problem with Dirichlet boundary condition we prove global well-posedness and scattering for all initial data in the energy space. 
Rowan Killip, Monica Visan, and Xiaoyi Zhang
math.AP