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The defocusing energy-critical Klein-Gordon-Hartree equation

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Miao Q., Zheng J.

Colloquium Mathematicum

2015

tom 140

nr 1

31-58

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.

Ograniczanie wyników

1 Colloquium Mathematicum

1 Miao Q.

1 Zheng J.

1 2015

Wyniki wyszukiwania

The defocusing energy-critical Klein-Gordon-Hartree equation