  We consider weakly regular Gowdy-symmetric spacetimes on T3 satisfying the
Einstein-Euler equations of general relativity, and we solve the initial value
problem when the initial data set has bounded variation, only, so that the
corresponding spacetime may contain impulsive gravitational waves as well as
shock waves. By analyzing, both, future expanding and future contracting
spacetimes, we establish the existence of a global foliation by spacelike
hypersurfaces so that the time function coincides with the area of the surfaces
of symmetry and asymptotically approaches infinity in the expanding case and
zero in the contracting case. More precisely, the latter property in the
contracting case holds provided the mass density does not exceed a certain
threshold, which is a natural assumption since certain exceptional data with
sufficiently large mass density are known to give rise to a Cauchy horizon, on
which the area function attains a positive value. An earlier result by LeFloch
and Rendall assumed a different class of weak regularity and did not determine
the range of the area function in the contracting case. Our method of proof is
based on a version of the random choice scheme adapted to the Einstein
equations for the symmetry and regularity class under consideration. We also
analyze the Einstein constraint equations under weak regularity.
