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arXiv · 0904.4749

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

Oana Ivanovici·Fabrice Planchon
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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.

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Oana Ivanovici, Fabrice Planchon. 2009-04-30. On the energy critical Schrodinger equation in 3D non-trapping domains. https://doi.org/10.1016/j.anihpc.2010.04.001

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