摘要
In this paper, we consider the defocusing, energy-critical Hartree equation with harmonic potential for the radial data in all dimensions (n ≥ 5) and show the global well-posedness and scattering theory in the space Σ = H1 ∩ F H1. 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.
源语言 | 英语 |
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页(从-至) | 2821-2840 |
页数 | 20 |
期刊 | Nonlinear Analysis, Theory, Methods and Applications |
卷 | 72 |
期 | 6 |
DOI | |
出版状态 | 已出版 - 15 5月 2009 |
已对外发布 | 是 |
指纹
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Wu, H., & Zhang, J. (2009). Energy-critical Hartree equation with harmonic potential for radial data. Nonlinear Analysis, Theory, Methods and Applications, 72(6), 2821-2840. https://doi.org/10.1016/j.na.2009.11.026