We prove that the quintic Schrödinger equation with Dirichlet boundary conditions is locally well posed for data on any smooth, non-trapping domain . The key ingredient is a smoothing effect in 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}, volume = {27}, year = {2010}, pages = {1153-1177}, doi = {10.1016/j.anihpc.2010.04.001}, mrnumber = {2683754}, zbl = {1200.35066}, language = {en}, url = {http://dml.mathdoc.fr/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, Tome 27 (2010) pp. 1153-1177. doi : 10.1016/j.anihpc.2010.04.001. http://gdmltest.u-ga.fr/item/AIHPC_2010__27_5_1153_0/
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