JournalsaihpcVol. 27, No. 5pp. 1153–1177

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

  • Oana Ivanovici

    Université Paris-Sud, Orsay, Mathématiques, Bat. 430, 91405 Orsay Cedex, France

  • Fabrice Planchon

    Laboratoire Analyse, Géométrie & Applications, UMR 7539 du CNRS, Institut Galilée, Université Paris 13, 99 avenue J.B. Clément, F-93430 Villetaneuse, France
On the energy critical Schrödinger equation in 3D non-trapping domains cover
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Abstract

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.

Cite this article

Oana Ivanovici, Fabrice Planchon, On the energy critical Schrödinger equation in 3D non-trapping domains. Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), no. 5, pp. 1153–1177

DOI 10.1016/J.ANIHPC.2010.04.001