The defocusing energy-critical Klein-Gordon-Hartree equation

• Autorzy: Qianyun Miao , Jiqiang Zheng
• Języki publikacji: EN

Abstrakty

EN

We study the scattering theory for the defocusing energy-critical Klein-Gordon equation with a cubic convolution $u_{tt} - Δu + u + (|x|^{-4} ∗ |u|²)u = 0$ 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.

Kategorie tematyczne

• 35Q40: PDEs in connection with quantum mechanics
• 81U99: None of the above, but in this section
• 35P25: Scattering theory
• 35B40: Asymptotic behavior of solutions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2015
• Tom: 140
• Numer: 1
• Strony: 31-58

Daty

wydano

2015

Twórcy

autor

Qianyun Miao

• School of Mathematics and System Sciences, Beihang University, Beijing 100191, China

autor

Jiqiang Zheng

• Laboratoire de Mathématiques J. A. Dieudonné, Université Nice Sophia-Antipolis, 06108 Nice Cedex 02, France

Identyfikatory

DOI

10.4064/cm140-1-4