Global wellposedness for 2D quasilinear wave without Lorentz

TL;DR

This paper proves the global well-posedness of 2D quasilinear wave equations with null-form nonlinearities without relying on Lorentz boost vector fields, expanding the understanding of wave equation behavior.

Contribution

It introduces a novel approach to establish global well-posedness without Lorentz boosts for 2D quasilinear wave equations with null-form nonlinearities.

Findings

Global existence of solutions established

Method avoids Lorentz boost vector fields

Applicable to 2D quasilinear wave equations with null forms

Abstract

We consider the two-dimensional quasilinear wave equations with standard null-form type quadratic nonlinearities. We prove global wellposedness without using the Lorentz boost vector fields.