Geodesic
The defocusing energy-critical Klein–Gordon–Hartree equation
Qianyun Miao 1   ; Jiqiang Zheng 2
1 School of Mathematics and System Sciences Beihang University Beijing 100191, China
2 Laboratoire de Mathématiques J. A. Dieudonné Université Nice Sophia-Antipolis 06108 Nice Cedex 02, France
Colloquium Mathematicum, Tome 140 (2015) no. 1, pp. 31-58 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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We study the scattering theory for the defocusing energy-critical Klein–Gordon equation with a cubic convolution $u_{tt}-\varDelta u+u+(|x|^{-4}\ast |u|^2)u=0$ in spatial dimension $d \geq 5$. 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.
DOI : 10.4064/cm140-1-4
Keywords: study scattering theory defocusing energy critical klein gordon equation cubic convolution vardelta ast spatial dimension geq utilize strategy ibrahim derived concentration compactness ideas proof global well posedness scattering reduced disproving existence soliton like solution employing technique pausader consider virial type identity direction orthogonal momentum vector exclude solution

Qianyun Miao  1   ; Jiqiang Zheng  2

1 School of Mathematics and System Sciences Beihang University Beijing 100191, China
2 Laboratoire de Mathématiques J. A. Dieudonné Université Nice Sophia-Antipolis 06108 Nice Cedex 02, France 
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Qianyun Miao; Jiqiang Zheng. The defocusing energy-critical Klein–Gordon–Hartree equation. Colloquium Mathematicum, Tome 140 (2015) no. 1, pp. 31-58. doi: 10.4064/cm140-1-4

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