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

Miao, Changxing; Xu, Guixiang; Zhao, Lifeng

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

Authors

Miao, Changxing

Xu, Guixiang

Zhao, Lifeng

Description

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.
23 pages, 1 figure