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

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.