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arXiv · 0704.0665

Global well-posedness and scattering for the energy-critical, defocusing Hartree equation for radial data

Changxing Miao·Guixiang Xu·Lifeng Zhao
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Abstract

We consider the defocusing, $\dot{H}^1$-critical Hartree equation for the radial data in all dimensions $(n\geq 5)$. We show the global well-posedness and scattering results in the energy space. The new ingredient in this paper is that we first take advantage of the term $\displaystyle - \int_{I}\int_{|x|\leq A|I|^{1/2}}|u|^{2}Δ\Big(\frac{1}{|x|}\Big)dxdt$ in the localized Morawetz identity to rule out the possibility of energy concentration, instead of the classical Morawetz estimate dependent of the nonlinearity.

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Changxing Miao, Guixiang Xu, Lifeng Zhao. 2007-04-15. Global well-posedness and scattering for the energy-critical, defocusing Hartree equation for radial data. https://doi.org/10.1016/j.jfa.2007.09.008

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