Finite time blow up to critical semilinear wave equation outside the ball in 3-D

Abstract

In this paper we study the initial boundary value problem of critical semilinear wave equation with small initial data in 3-D. Blow up result will be established no matter how small the data are. We find a radial and positive solution of the corresponding linear problem, then our blow up result follows from the idea of Zhou and Han (2014). What is more, we get the upper bound of the lifespan estimate.