On the energy critical Schrödinger equation in 3D non-trapping domains
Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 5, pp. 1153-1177.

We prove that the quintic Schrödinger equation with Dirichlet boundary conditions is locally well posed for H 0 1 (Ω) data on any smooth, non-trapping domain Ω 3 . The key ingredient is a smoothing effect in L x 5 (L t 2 ) for the linear equation. We also derive scattering results for the whole range of defocusing sub quintic Schrödinger equations outside a star-shaped domain.

@article{AIHPC_2010__27_5_1153_0,
     author = {Ivanovici, Oana and Planchon, Fabrice},
     title = {On the energy critical {Schr\"odinger} equation in {3\protect\emph{D}} non-trapping domains},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     pages = {1153--1177},
     publisher = {Elsevier},
     volume = {27},
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     year = {2010},
     doi = {10.1016/j.anihpc.2010.04.001},
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Ivanovici, Oana; Planchon, Fabrice. On the energy critical Schrödinger equation in 3D non-trapping domains. Annales de l'I.H.P. Analyse non linéaire, Volume 27 (2010) no. 5, pp. 1153-1177. doi : 10.1016/j.anihpc.2010.04.001. http://archive.numdam.org/articles/10.1016/j.anihpc.2010.04.001/

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