Journal article
On the Dispersive Estimate for the Dirichlet Schrodinger Propagator and Applications to Energy Critical NLS
Canadian journal of mathematics, Vol.66(5), pp.1110-1142
10/01/2014
DOI: 10.4153/CJM-2014-002-0
Abstract
We consider the obstacle problem for the Schrodinger evolution in the exterior of the unit ball with Dirichlet boundary condition. Under radial symmetry we compute explicitly the fundamental solution for the linear Dirichlet Schrodinger propagator e(it Delta D) and give a robust algorithm to prove sharp L-1 -> L-infinity dispersive estimates. We showcase the analysis in dimensions n = 5, 7. As an application, we obtain global well-posedness and scattering for defocusing energy-critical NLS on Omega = R-n\<(B(0, 1) )over bar> with Dirichlet boundary condition and radial data in these dimensions.
Details
- Title: Subtitle
- On the Dispersive Estimate for the Dirichlet Schrodinger Propagator and Applications to Energy Critical NLS
- Creators
- Dong Li - University of British ColumbiaGuixiang Xu - Institute of Applied PhysicsXiaoyi Zhang - University of Iowa
- Resource Type
- Journal article
- Publication Details
- Canadian journal of mathematics, Vol.66(5), pp.1110-1142
- DOI
- 10.4153/CJM-2014-002-0
- ISSN
- 0008-414X
- eISSN
- 1496-4279
- Publisher
- CANADIAN MATHEMATICAL SOC
- Number of pages
- 33
- Grant note
- 11171033; 11231006 / NSF of China; National Natural Science Foundation of China (NSFC) DMS-1128155 / NSF; National Science Foundation (NSF) Alfred P. Sloan Research fellowship; Alfred P. Sloan Foundation NSERC Discovery grant; Natural Sciences and Engineering Research Council of Canada (NSERC) University of British Columbia
- Language
- English
- Date published
- 10/01/2014
- Academic Unit
- Mathematics
- Record Identifier
- 9984242421202771
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