Global existence for some 4-D quasilinear wave equations with low regularity

TL;DR

This paper establishes the global existence of solutions for certain 4-D quasilinear wave equations with low regularity initial data, using advanced energy and trace estimates.

Contribution

It introduces a novel approach combining local energy estimates with variable coefficients and trace estimates for low-regularity data.

Findings

Proves global existence for specific 4-D quasilinear wave equations.

Handles small, radial initial data in low regularity spaces.

Develops new energy estimate techniques for variable coefficient equations.

Abstract

In this paper, we prove the global existence for some 4-D quasilinear wave equations with small, radial data in $H^{3}\times H^{2}$. The main idea is to exploit local energy estimates with variable coefficients, together with the trace estimates.