Global well-posedness and scattering for the defocusing, energy -critical, nonlinear Schr{ö}dinger equation in the exterior of a convex obstacle when $d = 4$

Details Global well-posedness and scattering for the defocusing, energy -critical, nonlinear Schr{ö}dinger equation in the exterior of a convex obstacle when $d = 4$ Global well-posedness and scattering for the defocusing, energy -critical, nonlinear Schr{ö}dinger equation in the exterior of a convex obstacle when $d = 4$

2011-12-04

arxiv.org/abs/1112.0710v1

Mathematics

Analysis of PDEs

31 pages

Scientific paper

In this paper we prove that the energy - critical nonlinear Schr{\"o}dinger
equation in the domain exterior to a convex obstacle is globally well - posed
and scattering for initial data having finite energy. To prove this we utilize
frequency localized Morawetz estimates adapted to an exterior domain.

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