Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
842662 | Nonlinear Analysis: Theory, Methods & Applications | 2010 | 20 Pages |
Abstract
In this paper, we consider the defocusing, energy-critical Hartree equation with harmonic potential for the radial data in all dimensions (n≥5)(n≥5) and show the global well-posedness and scattering theory in the space Σ=H1∩FH1Σ=H1∩FH1. We take advantage of some symmetry of the Hartree nonlinearity to exploit the derivative-like properties of the Galilean operators and obtain the energy control as well. Based on Bourgain and Tao’s approach, we use a localized Morawetz identity to show the global well-posedness. A key decay estimate comes from the linear part of the energy rather than the nonlinear part, which finally helps us to complete the scattering theory.
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Authors
Haigen Wu, Junyong Zhang,