Schwarzschild时空中带非线性记忆项的波动方程解的破裂

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

本文研究Schwarzschild时空中带非线性记忆项的波动方程径向解的破裂.首先在ReggeWheeler坐标下得到与原问题等价的方程.然后引入两个试探函数,并结合方程的解构造泛函.最后通过一个迭代过程证明:当非线性记忆项中的指标满足一定条件时,不管初值多么小,解在有限时间内破裂.

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.