GLOBAL WELL-POSEDNESS AND SCATTERING FOR DEFOCUSING ENERGY-CRITICAL NLS IN THE EXTERIOR OF BALLS WITH RADIAL DATA

Dong Li; Hart Smith; Xiaoyi Zhang

doi:10.4310/MRL.2012.v19.n1.a17

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GLOBAL WELL-POSEDNESS AND SCATTERING FOR DEFOCUSING ENERGY-CRITICAL NLS IN THE EXTERIOR OF BALLS WITH RADIAL DATA

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GLOBAL WELL-POSEDNESS AND SCATTERING FOR DEFOCUSING ENERGY-CRITICAL NLS IN THE EXTERIOR OF BALLS WITH RADIAL DATA

Dong Li, Hart Smith and Xiaoyi Zhang

Mathematical research letters, Vol.19(1), pp.213-232

01/01/2012

DOI: 10.4310/MRL.2012.v19.n1.a17

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Abstract

We consider the defocusing energy-critical nonlinear Schrodinger (NLS) in the exterior of the unit ball in three dimensions. For the initial value problem with Dirichlet boundary condition, we prove global well-posedness and scattering with large radial initial data in the Sobolev space (H)over dot(0)(1). We also point out that the same strategy can be used to treat the energy-supercritical NLS in the exterior of balls with Dirichlet boundary condition and radial (H)over dot(0)(1) initial data.

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Details

Title: Subtitle: GLOBAL WELL-POSEDNESS AND SCATTERING FOR DEFOCUSING ENERGY-CRITICAL NLS IN THE EXTERIOR OF BALLS WITH RADIAL DATA
Creators: Dong Li - University of British Columbia
Hart Smith - University of Washington
Xiaoyi Zhang - Chinese Academy of Sciences
Resource Type: Journal article
Publication Details: Mathematical research letters, Vol.19(1), pp.213-232
Publisher: INT PRESS BOSTON, INC
DOI: 10.4310/MRL.2012.v19.n1.a17
ISSN: 1073-2780
eISSN: 1945-001X
Number of pages: 20
Grant note: start up fund in UBC DMS-0654415 / NSF Alfred P. Sloan Research Fellowship
Language: English
Date published: 01/01/2012
Academic Unit: Mathematics
Record Identifier: 9984241150202771

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