Local decay of waves on asymptotically flat stationary space-times
Local decay of waves on asymptotically flat stationary space-times
复制标题
DOI：
10.1353/ajm.2013.0012
复制
发表时间：
2009-10
影响因子：
1.7
通讯作者：
D. Tataru
中科院分区：
文献类型：
--
作者：
D. Tataru
摘要：本文研究了三维空间中一类平稳渐近平坦背景下波动方程解的点向衰减性质。在均匀能量界和局部能量衰减的弱形式随时间向前发展的假设下，我们建立了线性波的$t^{-3}$局部均匀衰减率。这项工作的动机是关于Schwarzschild和Kerr背景下线性波的衰减率的公开问题，其中这种衰减率已经由R. Price推测出来。我们的结果适用于这两种情况。
Author(s): Tataru, Daniel | Abstract: In this article we study the pointwise decay properties of solutions to the wave equation on a class of stationary asymptotically flat backgrounds in three space dimensions. Under the assumption that uniform energy bounds and a weak form of local energy decay hold forward in time we establish a $t^{-3}$ local uniform decay rate for linear waves. This work was motivated by open problems concerning decay rates for linear waves on Schwarzschild and Kerr backgrounds, where such a decay rate has been conjectured by R. Price. Our results apply to both of these cases.