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

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