极值克尔时空中轴对称波的物理空间估计值

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis Pub Date : 2024-09-12 DOI:10.1016/j.jfa.2024.110668

Elena Giorgi, Jingbo Wan

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引用次数: 0

摘要

我们研究了极值克尔背景上波方程的轴对称解，并通过分析得到了综合局部能量衰减（或莫拉维兹估计值）。极值克尔中轴对称波的能量有界性和莫拉维兹估计值最早是由 Aretakis 通过构建频率局部电流（特别是用于表达陷波退行性）得到的。在此，我们将斯托金在次极值情况下引入的方法扩展到极值克尔，通过纯经典电流简化了阿雷塔基斯对莫拉维兹估计值的推导。

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Physical-space estimates for axisymmetric waves on extremal Kerr spacetime

We study axisymmetric solutions to the wave equation on extremal Kerr backgrounds and obtain integrated local energy decay (or Morawetz estimates) through an analysis exclusively in physical-space. Boundedness of the energy and Morawetz estimates for axisymmetric waves in extremal Kerr were first obtained by Aretakis [13] through the construction of frequency-localized currents used in particular to express the trapping degeneracy. Here we extend to extremal Kerr a method introduced by Stogin [63] in the sub-extremal case, simplifying Aretakis' derivation of Morawetz estimates through purely classical currents.

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来源期刊

Journal of Functional Analysis 数学-数学

CiteScore

3.20

自引率

5.90%

发文量

271

审稿时长

7.5 months

期刊介绍： The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published. Research Areas Include: • Significant applications of functional analysis, including those to other areas of mathematics • New developments in functional analysis • Contributions to important problems in and challenges to functional analysis