Large data global existence for coupled massive-massless wave-type systems

TL;DR

This paper proves global existence and describes the long-term behavior of solutions for 3D coupled wave systems involving both massive and massless fields, even with large initial data.

Contribution

It establishes the first global existence results for large data in coupled massive-massless wave systems like KGZ and DKG.

Findings

Global solutions exist for large initial data

Asymptotic behavior of solutions characterized

Massless or massive fields can be large without loss of control

Abstract

We consider 3D Klein-Gordon-Zakharov (KGZ) and Dirac-Klein-Gordon (DKG) systems, where a common feature is that there exist both massless and massive fields in each system. We establish global existence and asymptotic behavior for both systems with a class of large data. More precisely, in the KGZ system, we allow the massless field to be large, while in the DKG system we allow the massive field to be large.