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

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.

preprint2009arXivOpen access
Oana IvanoviciFabrice Planchon
math.AP
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Oana IvanoviciFabrice Planchon

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