Blow up of solutions of semilinear wave equations related to nonlinear waves in de Sitter spacetime

TL;DR

This paper investigates finite-time blow-up phenomena for nonlinear wave equations in de Sitter spacetime, establishing conditions and lifespan bounds, with results applicable to similar equations in FLRW spacetime.

Contribution

It demonstrates blow-up for a broad class of nonlinear wave equations in de Sitter spacetime and provides lifespan estimates, extending understanding of wave behavior in cosmological models.

Findings

Finite-time blow-up occurs for arbitrary power nonlinearities.

Blow-up conditions match those in FLRW spacetime.

Lifespan bounds are established for solutions.

Abstract

Consider a nonlinear wave equation for a massless scalar field with self-interaction in the spatially flat de Sitter spacetime. We show that blow-up in a finite time occurs for the equation with arbitrary power nonlinearity as well as upper bounds of the lifespan of blow-up solutions.The blow-up condition is the same as in the accelerated expanding Friedmann-Lema\^itre-Robertson-Walker (FLRW) spacetime. We also show the same results for the space derivative nonlinear term.