The weak null condition on Kerr backgrounds

TL;DR

This paper proves global existence and decay for a system of wave equations on Kerr black hole backgrounds satisfying the weak null condition, assuming small initial data.

Contribution

It establishes the first global existence results for such systems on Kerr backgrounds under the weak null condition.

Findings

Global existence of solutions

Pointwise decay estimates

Validation of weak null condition on Kerr backgrounds

Abstract

We study a system of semilinear wave equations on Kerr backgrounds that satisfies the weak null condition. Under the assumption of small initial data, we prove global existence and pointwise decay estimates.