标题： 爱因斯坦-欧拉时空在T3上的全局叶状结构 显示英文标题

标题： A global foliation of Einstein-Euler spacetimes with Gowdy-symmetry on T3

摘要： 我们研究在T3上Gowdy对称性假设下广义相对论的Einstein-Euler方程的初值问题，并构造具有低正则性的物质时空。 这些时空既包含度规中的冲击引力波（例如以光速传播的Dirac质量曲率奇点），又包含流体中的冲击波（即以大约声速传播的不连续性）。 给定一个初始数据集，我们建立未来发展的存在性，并提供了一个全局的叶状结构，该结构以一个全局且几何定义的时间函数为基准，与对称群轨道的面积密切相关。 主要困难在于对初始数据集所作的低正则性假设，这需要Einstein-Euler方程的分布形式表述。 显示英文摘要

摘要： We investigate the initial value problem for the Einstein-Euler equations of general relativity under the assumption of Gowdy symmetry on T3, and we construct matter spacetimes with low regularity. These spacetimes admit, both, impulsive gravitational waves in the metric (for instance, Dirac mass curvature singularities propagating at light speed) and shock waves in the fluid (i.e., discontinuities propagating at about the sound speed). Given an initial data set, we establish the existence of a future development and we provide a global foliation in terms of a globally and geometrically defined time-function, closely related to the area of the orbits of the symmetry group. The main difficulty lies in the low regularity assumed on the initial data set which requires a distributional formulation of the Einstein-Euler equations.