Ill-posedness in the Einstein equations

被引：21

作者：

Frittelli, S ^{[1
]}

Gomez, R

机构：

[1] Duquesne Univ, Dept Phys, Pittsburgh, PA 15282 USA

[2] Univ Pittsburgh, Dept Phys & Astron, Pittsburgh, PA 15260 USA

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 2000年 / 41卷 / 08期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1063/1.533423

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

It is shown that the formulation of the Einstein equations widely in use in numerical relativity, namely, the standard ADM form, as well as some of its variations (including the most recent conformally-decomposed version), suffers from a certain but standard type of ill-posedness. Specifically, the norm of the solution is not bounded by the norm of the initial data irrespective of the data. A long-running numerical experiment is performed as well, showing that the type of ill-posedness observed may not be serious in specific practical applications, as is known from many numerical simulations. (C) 2000 American Institute of Physics. [S0022- 2488(00)00108-0].

引用

页码：5535 / 5549

页数：15

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