Finite time blow up for a wave equation with nonlinear memory in Schwarzschild spacetime

Abstract

In this work, we study the Cauchy problem of wave equation with nonlinear memory in Schwarzschild spacetime. Blow up result will be established when the power p of the memory and the data satisfy some conditions. For this purpose, we use two test functions to construct a functional. After that by introducing an iteration argument we conclude that the functional satisfies the conditions of Kato type lemma.