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, p. 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 3D non-trapping domains},
     journal = {Annales de l'I.H.P. Analyse non lin\'eaire},
     publisher = {Elsevier},
     volume = {27},
     number = {5},
     year = {2010},
     pages = {1153-1177},
     doi = {10.1016/j.anihpc.2010.04.001},
     zbl = {1200.35066},
     mrnumber = {2683754},
     language = {en},
     url = {http://www.numdam.org/item/AIHPC_2010__27_5_1153_0}
}
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://www.numdam.org/item/AIHPC_2010__27_5_1153_0/

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