On the energy critical Schrodinger equation in 3D non-trapping domains

Details On the energy critical Schrodinger equation in 3D non-trapping domains On the energy critical Schrodinger equation in 3D non-trapping domains

2009-04-30

arxiv.org/abs/0904.4749v3

Mathematics

Analysis of PDEs

Final version (fixed spectral localization issues in section 3.1.2, corrected some typos), 34 pages

Scientific paper

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.

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