Dynamic of Threshold Solutions for Energy-Critical NlS

. We consider the energy-critical non-linear focusing Schrödinger equation in dimension N = 3, 4, 5. An explicit stationary solution, W , of this equation is known. In [KeM], the energy E ( W ) has been shown to be a threshold for the dynamical behavior of solutions of the equation. In the present a...

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Bibliographic Details
Published inGeometric and functional analysis Vol. 18; no. 6; pp. 1787 - 1840
Main Authors Duyckaerts, Thomas, Merle, Frank
Format Journal Article
LanguageEnglish
Published Basel Birkhäuser-Verlag 01.03.2009
Subjects
Analysis
Mathematics
Mathematics and Statistics
Nonlinear wave equation
asymptotic behavior
scattering
35L70
35P25
blow-up
35B30
35B40
energy-critical
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Summary:. We consider the energy-critical non-linear focusing Schrödinger equation in dimension N = 3, 4, 5. An explicit stationary solution, W , of this equation is known. In [KeM], the energy E ( W ) has been shown to be a threshold for the dynamical behavior of solutions of the equation. In the present article, we study the dynamics at the critical level E ( u ) = E ( W ) and classify the corresponding solutions. This gives in particular a dynamical characterization of W .
ISSN:1016-443X
1420-8970
DOI:10.1007/s00039-009-0707-x