Pointwise decay for semilinear wave equations on Kerr spacetimes

TL;DR

This paper establishes optimal pointwise decay estimates for solutions to semilinear wave equations with powers $p \\geq 3$ on Kerr spacetimes with small angular momentum and initial data.

Contribution

It provides the first proof of optimal decay bounds for semilinear wave equations on Kerr backgrounds with small angular momentum.

Findings

Optimal pointwise decay bounds are proven for solutions.

Results apply to Kerr spacetimes with small angular momentum.

The decay estimates are sharp and match known linear decay rates.

Abstract

In this article we prove optimal pointwise bounds for solutions to the semilinear wave equation with integer powers $p\geq 3$ on Kerr backgrounds with small angular momentum and small initial data.