SCATTERING PROPERTY FOR A SYSTEM OF KLEIN-GORDON EQUATIONS WITH ENERGY
BELOW GROUND STATE
Abstract
In the previous work [6], we classified the solutions to a family of
systems of Klein-Gordon equations with non-negative energy below the
ground state into two parts: one blows up in finite time while the other
extends to a global solution. In the present work, we strengthen this
result, showing that these global solutions are indeed scattering in the
energy space. Here we adapted Kenig-Merle’s concentration-compactness
approach to the system.