Semilinear wave equations on accelerated expanding FLRW spacetimes

Abstract

We identify a large class of systems of semilinear wave equations, on fixed accelerated expanding FLRW spacetimes, with nearly flat 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 “blowup” equations (whose future blowup 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.