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 {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}, number = {5}, year = {2010}, doi = {10.1016/j.anihpc.2010.04.001}, mrnumber = {2683754}, zbl = {1200.35066}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.anihpc.2010.04.001/} }
TY - JOUR AU - Ivanovici, Oana AU - Planchon, Fabrice TI - On the energy critical Schrödinger equation in 3D non-trapping domains JO - Annales de l'I.H.P. Analyse non linéaire PY - 2010 SP - 1153 EP - 1177 VL - 27 IS - 5 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.anihpc.2010.04.001/ DO - 10.1016/j.anihpc.2010.04.001 LA - en ID - AIHPC_2010__27_5_1153_0 ER -
%0 Journal Article %A Ivanovici, Oana %A Planchon, Fabrice %T On the energy critical Schrödinger equation in 3D non-trapping domains %J Annales de l'I.H.P. Analyse non linéaire %D 2010 %P 1153-1177 %V 27 %N 5 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.anihpc.2010.04.001/ %R 10.1016/j.anihpc.2010.04.001 %G en %F 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) no. 5, pp. 1153-1177. doi : 10.1016/j.anihpc.2010.04.001. http://www.numdam.org/articles/10.1016/j.anihpc.2010.04.001/
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