Semilinear wave equations on accelerated expanding FLRW spacetimes

TL;DR

This paper proves small data global existence and decay bounds for a broad class of semilinear wave equations on accelerated expanding FLRW spacetimes, including wave maps and blow-up equations.

Contribution

It identifies a large class of semilinear wave systems on expanding FLRW spacetimes with proven global well-posedness and decay, extending previous results to more general equations.

Findings

Proved small data global existence for the class of systems.

Established sharp decay upper bounds.

Included general wave maps and blow-up equations in the analysis.

Abstract

We identify a large class of systems of semilinear wave equations, on fixed accelerated expanding FLRW spacetimes, with nearly at spatial slices, for which we prove small data future global well-posedness. The family of systems we consider is large in the sense that, among other examples, it includes general wave maps, as well as natural generalizations of some of Fritz John's "blow up" equations (whose future blow up disappears, in our setting, as a consequence of the spacetime expansion). We also establish decay upper bounds, which are sharp within the family of systems under analysis.