Scattering for solutions of NLS in the exterior of a 2d star--shaped obstacle
arXiv:1111.0277
Abstract
We prove that solutions to non-linear Schrödinger equations in two dimensions and in the exterior of a bounded and smooth star-shaped obstacle scatter in the energy space. The non-linear potential is defocusing and grows at least as the quintic power.
Final version to appear in Math. Res. Lett