Rough solutions of the Einstein-vacuum equations

• 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.2005.161.1143
• 发表日期: 2005
• 页码: 1143-1193
• 关键词: linear wave-equations; nonsmooth coefficients; strichartz; REGULARITY; counterexamples; Operators

摘要

This is the first in a series of 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. Following [Kl-Ro] we develop new analytic methods based on Strichartz-type inequalities which result in a gain of half a derivative relative to the classical result. Our methods blend paradifferential techniques with a geometric approach to the derivation of decay estimates. The latter allows us to take full advantage of the specific structure of the Einstein equations.