Global well-posedness and scattering for the energy-critical, defocusing Hartree equation for radial data
| dc.creator | Miao, Changxing | |
| dc.creator | Xu, Guixiang | |
| dc.creator | Zhao, Lifeng | |
| dc.date | 2007-04-05 | |
| dc.date | 2007-04-15 | |
| dc.date.accessioned | 2026-07-07T10:08:18Z | |
| dc.date.available | 2026-07-07T10:08:18Z | |
| dc.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. | |
| dc.description | 23 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/0704.0665 | |
| dc.identifier | http://arxiv.org/abs/0704.0665 | |
| dc.identifier | Journal of Functional Analysis 253 (2007)605-627 | |
| dc.identifier | doi:10.1016/j.jfa.2007.09.008 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/170949 | |
| dc.subject | Analysis of PDEs | |
| dc.subject | Mathematical Physics | |
| dc.subject | 35Q40, 35Q55, 47J35 | |
| dc.title | Global well-posedness and scattering for the energy-critical, defocusing Hartree equation for radial data | |
| dc.type | text |