Peeling-off behavior of wave equation in the Vaidya spacetime

IF 0.5 4区数学 Q4 MATHEMATICS, APPLIED

Journal of Hyperbolic Differential Equations Pub Date : 2023-06-01 DOI:10.1142/s021989162350011x

Armand Coudray

引用次数: 0

Abstract

We study the peeling for the wave equation on the Vaidya spacetime following the approach developed by Mason and Nicolas in Mason–Nicolas 2009. The idea is to encode the regularity at null infinity of the rescaled field, characterized by Sobolev-type norms, in terms of corresponding function spaces of initial data. All function spaces are obtained from energy fluxes associated with an observer constructed from the Morawetz vector field on Minkowski spacetime. We combine conformal techniques and energy estimates to obtain the optimal classes of initial data ensuring a given regularity of the rescaled field. The classes of data are equivalent to those obtained on Minkowski and Schwarzschild spacetimes in that they impose the same decay at infinity and regularity.

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波动方程在Vaidya时空中的剥离行为

根据Mason和Nicolas在Mason–Nicolas 2009中提出的方法，我们研究了Vaidya时空上波动方程的剥离。其思想是根据初始数据的相应函数空间，对以Sobolev型范数为特征的重缩放场在零无穷大处的正则性进行编码。所有函数空间都是从与观测者相关的能量通量中获得的，该观测者是由闵可夫斯基时空上的Morawetz矢量场构建的。我们将保角技术和能量估计相结合，以获得最佳的初始数据类别，确保重新缩放场的给定规则性。这类数据与在闵可夫斯基和史瓦西时空中获得的数据等价，因为它们在无穷大和正则性下施加了相同的衰减。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Hyperbolic Differential Equations 数学-物理：数学物理

CiteScore

1.10

自引率

0.00%

发文量

审稿时长

24 months

期刊介绍： This journal publishes original research papers on nonlinear hyperbolic problems and related topics, of mathematical and/or physical interest. Specifically, it invites papers on the theory and numerical analysis of hyperbolic conservation laws and of hyperbolic partial differential equations arising in mathematical physics. The Journal welcomes contributions in: Theory of nonlinear hyperbolic systems of conservation laws, addressing the issues of well-posedness and qualitative behavior of solutions, in one or several space dimensions. Hyperbolic differential equations of mathematical physics, such as the Einstein equations of general relativity, Dirac equations, Maxwell equations, relativistic fluid models, etc. Lorentzian geometry, particularly global geometric and causal theoretic aspects of spacetimes satisfying the Einstein equations. Nonlinear hyperbolic systems arising in continuum physics such as: hyperbolic models of fluid dynamics, mixed models of transonic flows, etc. General problems that are dominated (but not exclusively driven) by finite speed phenomena, such as dissipative and dispersive perturbations of hyperbolic systems, and models from statistical mechanics and other probabilistic models relevant to the derivation of fluid dynamical equations. Convergence analysis of numerical methods for hyperbolic equations: finite difference schemes, finite volumes schemes, etc.