Lifespan of Solutions to Wave Equations on de Sitter Spacetime

TL;DR

This paper investigates the finite time blow-up and lifespan of solutions to nonlinear wave equations on de Sitter spacetime, introducing a new blow-up criterion that extends previous results and providing lifespan estimates.

Contribution

It introduces a generalized blow-up criterion for nonlinear wave equations on de Sitter spacetime and derives lifespan estimates for solutions.

Findings

New blow-up criterion generalizing Sideris's work

Lifespan estimates for solutions to nonlinear wave equations on de Sitter spacetime

Finite time blow-up results for specific nonlinearities

Abstract

In this paper, we consider the finite time blow up of solutions for the following two kinds of nonlinear wave equations on de Sitter spacetime \begin{eqnarray*} &&\square_g=F(u),\\ &&\square_g=F(\partial_tu,\nabla u). \end{eqnarray*} This proof is based on a new blow up criterion, which generalize the blow up criterion in Sideris \cite{Sider}. Furthermore, we give the lifespan estimate of solutions for the problems.