We consider scattering properties of the critical nonlinear system of wave equations with Hamilton structure ⎧uₜₜ - Δu = -F₁(|u|²,|v|²)u, ⎨ ⎩vₜₜ - Δv = -F₂(|u|²,|v|²)v, for which there exists a function F(λ,μ) such that ∂F(λ,μ)/∂λ = F₁(λ,μ), ∂F(λ,μ)/∂μ = F₂(λ,μ). By using the energy-conservation law over the exterior of a truncated forward light cone and a dilation identity, we get a decay estimate for the potential energy. The resulting global-in-time estimates imply immediately the existence of the wave operators and the scattering operator.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm106-1-6,
author = {Changxing Miao and Youbin Zhu},
title = {Scattering theory for a nonlinear system of wave equations with critical growth},
journal = {Colloquium Mathematicae},
volume = {106},
year = {2006},
pages = {69-81},
zbl = {1100.35062},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm106-1-6}
}
Changxing Miao; Youbin Zhu. Scattering theory for a nonlinear system of wave equations with critical growth. Colloquium Mathematicae, Tome 106 (2006) pp. 69-81. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm106-1-6/