The causal structure of microlocalized rough Einstein metrics

• 成果类型: Article
• 署名作者: Klainerman, S; Rodnianski, I
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2005.161.1195
• 发表日期: 2005
• 页码: 1195-1243
• 关键词: linear wave-equations; nonsmooth coefficients; strichartz; Operators

摘要

This is the second in a series of three papers in which we initiate the study of very rough solutions to the initial value problem for the Einstein vacuum equations expressed relative to wave coordinates. By very rough we mean solutions which cannot be constructed by the classical techniques of energy estimates and Sobolev inequalities. In this paper we develop the geometric analysis of the Eikonal equation for microlocalized rough Einstein metrics. This is a crucial step in the derivation of the decay estimates needed in the first paper.