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On the Dispersive Estimate for the Dirichlet Schrodinger Propagator and Applications to Energy Critical NLS
Journal article   Open access   Peer reviewed

On the Dispersive Estimate for the Dirichlet Schrodinger Propagator and Applications to Energy Critical NLS

Dong Li, Guixiang Xu and Xiaoyi Zhang
Canadian journal of mathematics, Vol.66(5), pp.1110-1142
10/01/2014
DOI: 10.4153/CJM-2014-002-0
url
https://doi.org/10.4153/CJM-2014-002-0View
Published (Version of record) Open Access

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.
Mathematics Physical Sciences Science & Technology

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