Blow up of solutions of semilinear wave equations in accelerated expanding Friedmann-Lema\^{i}tre-Robertson-Walker spacetime

TL;DR

This paper investigates the finite-time blow-up of solutions to nonlinear wave equations in accelerated expanding Friedmann-Lemaître-Robertson-Walker spacetimes, highlighting how the universe's expansion influences solution lifespan.

Contribution

It demonstrates blow-up phenomena for nonlinear wave equations in accelerated cosmological backgrounds and provides lifespan estimates, extending understanding beyond Minkowski spacetime.

Findings

Blow-up occurs in finite time for arbitrary power nonlinearities.

The scale factor significantly affects the lifespan of solutions.

Comparison with Minkowski spacetime reveals the impact of accelerated expansion.

Abstract

Consider a nonlinear wave equation for a massless scalar field with self-interaction in the spatially flat Friedmann-Lema\^{i}tre-Robertson-Walker spacetimes. For the case of accelerated expansion, 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. Comparing to the case of the Minkowski spacetime, we discuss how the scale factor affects the lifespan of blow-up solutions of the equation.