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

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

2007-04-05

arxiv.org/abs/0704.0665v2

Journal of Functional Analysis 253 (2007)605-627

Mathematics

Analysis of PDEs

23 pages, 1 figure

Scientific paper

10.1016/j.jfa.2007.09.008

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 $\displaystyle - \int_{I}\int_{|x|\leq A|I|^{1/2}}|u|^{2}\Delta \Big(\frac{1}{|x|}\Big)dxdt$ 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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