# Large data decay of Yang-Mills-Higgs fields on Minkowski and de Sitter spacetimes

## TL;DR

This paper extends decay estimates for Yang-Mills-Higgs fields from Minkowski space to de Sitter and Einstein cylinder spacetimes, establishing global bounds and decay rates for large data scenarios.

## Contribution

It introduces a method to transfer local $L^
abla$ estimates to global ones on the Einstein cylinder via conformal transformations, enabling large data well-posedness and decay results.

## Key findings

- Global $L^
abla$ estimates on Einstein cylinder
- Exponential decay on de Sitter space
- Inverse polynomial decay on Minkowski space

## Abstract

We extend Eardley and Moncrief's $L^\infty$ estimates for the conformally invariant Yang-Mills-Higgs equations to the Einstein cylinder. Our method is to first work on Minkowski space and localise their estimates, and then carry them to the Einstein cylinder by a conformal transformation. By patching local estimates together, we deduce global $L^\infty$ estimates on the cylinder, and extend Choquet-Bruhat and Christodoulou's small data well-posedness result to large data. Finally, by employing another conformal transformation, we deduce exponential decay rates for Yang-Mills-Higgs fields on de Sitter space, and inverse polynomial decay rates on Minkowski space.