Global solutions of quasilinear systems of Klein--Gordon equations in 3D

TL;DR

This paper proves global existence and scattering for small data solutions of quasilinear Klein-Gordon systems in 3D, and applies the results to establish stability of the Euler-Maxwell equations for electrons.

Contribution

It introduces new methods to handle quasilinear Klein-Gordon systems with different speeds and applies these to the Euler-Maxwell equations.

Findings

Established global existence and scattering for the systems.

Proved stability of the Euler-Maxwell equations for electrons.

Developed techniques for quasilinear systems with multiple speeds.

Abstract

We prove small data global existence and scattering for quasilinear systems of Klein-Gordon equations with different speeds, in dimension three. As an application, we obtain a robust global stability result for the Euler-Maxwell equations for electrons.