The defocusing energy-critical Klein-Gordon-Hartree equation

Qianyun Miao, and Jiqiang Zheng. "The defocusing energy-critical Klein-Gordon-Hartree equation." Colloquium Mathematicae 140.1 (2015): 31-58. <http://eudml.org/doc/283530>.

@article{QianyunMiao2015,
abstract = {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.},
author = {Qianyun Miao, Jiqiang Zheng},
journal = {Colloquium Mathematicae},
keywords = {nonlinear stability; Turing patterns; hysteresis; discontinuous solutions; bistability; diffusion-driven instability; spike solutions},
language = {eng},
number = {1},
pages = {31-58},
title = {The defocusing energy-critical Klein-Gordon-Hartree equation},
url = {http://eudml.org/doc/283530},
volume = {140},
year = {2015},
}

TY - JOUR
AU - Qianyun Miao
AU - Jiqiang Zheng
TI - The defocusing energy-critical Klein-Gordon-Hartree equation
JO - Colloquium Mathematicae
PY - 2015
VL - 140
IS - 1
SP - 31
EP - 58
AB - 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.
LA - eng
KW - nonlinear stability; Turing patterns; hysteresis; discontinuous solutions; bistability; diffusion-driven instability; spike solutions
UR - http://eudml.org/doc/283530
ER -