On the energy critical Schrodinger equation in 3D non-trapping domains
arXiv:0904.4749 · doi:10.1016/j.anihpc.2010.04.001
Abstract
We prove that the quintic Schrodinger equation with Dirichlet boundary conditions is locally well posed for H^{1}_{0} data on any smooth, non-trapping domain of R^3. The key ingredient is a smoothing effect in L^{5}_{x}L^{2}_{t} for the linear equation. We also derive scattering results for the whole range of defocusing sub-quintic Schrodinger equations outside star-shaped domains.
Final version (fixed spectral localization issues in section 3.1.2, corrected some typos), 34 pages