标题： CMCSH规范下爱因斯坦真空方程的粗糙解 显示英文标题

标题： Rough solutions of Einstein vacuum equations in CMCSH gauge

摘要： 本文中，我们在CMC空间谐调规范下，研究了Einstein真空方程Cauchy问题的非常粗糙解，并在$H^s, s>2$中得到了局部适定性结果。 我们方法的新颖之处在于，无需依赖于粗糙Einstein度规$\bg$的标准仿微分正则化，我们成功实现了交换向量场方法，从而直接证明了几何波动方程$\Box_\bg \phi=0$的Strichartz估计。 显示英文摘要

摘要： In this paper, we consider very rough solutions to Cauchy problem for the Einstein vacuum equations in CMC spacial harmonic gauge, and obtain the local well-posedness result in $H^s, s>2$. The novelty of our approach lies in that, without resorting to the standard paradifferential regularization over the rough, Einstein metric $\bg$, we manage to implement the commuting vector field approach to prove Strichartz estimate for geometric wave equation $\Box_\bg \phi=0$ directly.