Global existence for defocusing cubic NLS and Gross-Pitaevskii equations in three dimensional exterior domains

Details Global existence for defocusing cubic NLS and Gross-Pitaevskii equations in three dimensional exterior domains Global existence for defocusing cubic NLS and Gross-Pitaevskii equations in three dimensional exterior domains

2007-01-10

arxiv.org/abs/math/0701304v1

Mathematics

Analysis of PDEs

Scientific paper

We prove global wellposedness in the energy space of the defocusing cubic
nonlinear Schroedinger and Gross-Pitaevskii equations on the exterior of a
non-trapping domain in dimension 3. The main ingredient is a Strichartz
estimate obtained combining a semi-classical Strichartz estimate with a
smoothing effect on exterior domains.

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