We study the scattering theory for the defocusing energy-critical Klein-Gordon equation with a cubic convolution in spatial dimension d ≥ 5. We utilize the strategy of Ibrahim et al. (2011) derived from concentration compactness ideas to show that the proof of the global well-posedness and scattering can be reduced to disproving the existence of a soliton-like solution. Employing the technique of Pausader (2010), we consider a virial-type identity in the direction orthogonal to the momentum vector to exclude such a solution.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm140-1-4,
author = {Qianyun Miao and Jiqiang Zheng},
title = {The defocusing energy-critical Klein-Gordon-Hartree equation},
journal = {Colloquium Mathematicae},
volume = {139},
year = {2015},
pages = {31-58},
zbl = {1327.35182},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm140-1-4}
}
Qianyun Miao; Jiqiang Zheng. The defocusing energy-critical Klein-Gordon-Hartree equation. Colloquium Mathematicae, Tome 139 (2015) pp. 31-58. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm140-1-4/