论文标题
Minkowski时空在外部区域的稳定性
Stability of Minkowski spacetime in exterior regions
论文作者
论文摘要
1993年，Minkowski时空的全球稳定性在Christodoulou和Klainerman \ Cite \ Cite {Ch-kl}的著名作品中得到了证明。在2003年，Klainerman和Nicòlo\ cite {Kl-ni}在即将离去的零锥的外部的情况下，给出了Minkowski稳定性的第二个证据。在本文中，我们给出了\ cite {kl-ni}的新证明。与\ cite {kl-ni}相比，我们减少了证明中所需的衍生物数量，简化了最后一个切片的处理，并提供了对初始数据衰减的统一处理。同样，关于曲率估计的处理，我们用$ r^p $ - dafermos和rodnianski \ rodnianski \ cite {da-da-ro}的加权估计来替换\ cite {kl-ni}中使用的veTORFIEED方法。
In 1993, the global stability of Minkowski spacetime has been proven in the celebrated work of Christodoulou and Klainerman \cite{Ch-Kl} in a maximal foliation. In 2003, Klainerman and Nicòlo \cite{Kl-Ni} gave a second proof of the stability of Minkowski in the case of the exterior of an outgoing null cone. In this paper, we give a new proof of \cite{Kl-Ni}. Compared to \cite{Kl-Ni}, we reduce the number of derivatives needed in the proof, simplify the treatment of the last slice, and provide a unified treatment of the decay of initial data. Also, concerning the treatment of curvature estimates, we replace the vectorfield method used in \cite{Kl-Ni} by the $r^p$--weighted estimates of Dafermos and Rodnianski \cite{Da-Ro}.
