渐近平坦时空下爱因斯坦真空方程的积分破裂准则
An integral breakdown criterion for Einstein vacuum equations in the case of asymptotically flat spacetimes
摘要：
本文给出了爱因斯坦真空方程的一个积分破裂判据的证明。在S.Klainerman和I.Rodnianski最近的一篇文章中，作为一系列涉及新技术的文章的结果，证明了一种新的击穿判据。然而，在这篇文章中，作者提到，很可能证明一个涉及积分条件而不是逐点条件的更尖锐的结果。本文给出了这一改进的证明。此外，证明这一故障标准写在原来的文章中的一个叶理的常数平均曲率，我们将在这里提出一个最大的叶理，导致一些困难，由于非紧性的叶子这样的叶理和使用加权Sobolev规范。
英文摘要：
We will give in this paper the proof of an integral breakdown criterion for Einstein vacuum equations. In a recent article of S.Klainerman and I.Rodnianski a new breakdown criterion was proved as a result of a sequence of articles involving new techniques. However, in this article, the authors mentioned that it was likely possible to prove a sharper result involving an integral condition instead of a pointwise one. This paper is concerned with giving the proof of this improvement. Moreover the proof of this breakdown criterion was written in the original article for a foliation of constant mean curvature, we will present it here for a maximal foliation which leads to some difficulties due to the non-compacity of the leaves of such a foliation and the use of weighted Sobolev norms.
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