Global dynamics below the ground state energy for the Klein-Gordon-Zakharov system in the 3D radial case

TL;DR

This paper investigates the long-term behavior of solutions to the 3D radial Klein-Gordon-Zakharov system below the ground state energy, establishing criteria for scattering versus finite time blow-up.

Contribution

It provides a dichotomy result for the global dynamics of the system, distinguishing conditions leading to scattering or blow-up in the radial case.

Findings

Established scattering criteria below the ground state energy.

Proved finite time blow-up conditions for certain initial data.

Analyzed the system's behavior in the radial symmetry setting.

Abstract

We consider the global dynamics below the ground state energy for the Klein-Gordon-Zakharov system in the 3D radial case; and obtain the dichotomy between scattering and finite time blow up.