Almost global well-posedness for quasilinear strongly coupled wave-Klein-Gordon systems in two space dimensions

TL;DR

This paper establishes almost global well-posedness for certain quasilinear wave-Klein-Gordon systems in two dimensions with small, localized data, using a new robust analytical approach.

Contribution

It introduces a novel method to prove almost global well-posedness for strongly coupled wave-Klein-Gordon systems with minimal regularity and decay assumptions.

Findings

Proved almost global well-posedness for the systems.

Analyzed quadratic null form type nonlinearities.

Developed a new robust proof technique.

Abstract

We prove almost global well-posedness for quasilinear strongly coupled wave-Klein-Gordon systems with small and localized data in two space dimensions. We assume only mild decay on the data at infinity as well as minimal regularity. We systematically investigate all the possible quadratic null form type quasilinear strong coupling nonlinearities, and provide a new, robust approach for the proof. In a second paper we will complete the present results to full global well-posedness.