Article ID Journal Published Year Pages File Type
842662 Nonlinear Analysis: Theory, Methods & Applications 2010 20 Pages PDF
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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