Energy-critical Hartree equation with harmonic potential for radial data |
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Authors: | Haigen Wu Junyong Zhang |
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Institution: | a School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, Henan Province, 454000, China b The Graduate School of China Academy of Engineering Physics, P. O. Box 2101, Beijing, 100088, China |
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Abstract: | 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∩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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Keywords: | 35Q40 35Q55 47J35 |
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