Lifespan of Solutions to Wave Equations on de Sitter Spacetime

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.

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References in corpus (3)

• The Strauss conjecture on Kerr black hole backgrounds
• The Glassey conjecture on asymptotically flat manifolds
• The sharp upper bound of the lifespan of solutions to critical semilinear wave equations in high dimensions