  We develop a new perturbation theory (PT) treatment that can describe
gravitational dynamics of large-scale structure after shell-crossing in the
one-dimensional cosmological case. Starting with cold initial conditions, the
motion of matter distribution follows at early stages the single-stream regime,
which can, in one dimension, be described exactly by the first-order Lagrangian
perturbation, i.e. the Zel'dovich solution. However, the single-stream flow no
longer holds after shell-crossing and a proper account of the multi-stream flow
is essential for post-collapse dynamics. In this paper, extending previous work
by Colombi (2015, MNRAS 446, 2902), we present a perturbative description for
the multi-stream flow after shell-crossing in a cosmological setup. In
addition, we introduce an adaptive smoothing scheme to deal with the bulk
properties of phase-space structures. The filtering scales in this scheme are
linked to the next-crossing time in the post-collapse region, estimated from
our PT calculations. Our PT treatment combined with adaptive smoothing is
illustrated in several cases. Predictions are compared to simulations and we
find that post-collapse PT with adaptive smoothing reproduces the power
spectrum and phase-space structures remarkably well even at small scales, where
Zel'dovich solution substantially deviates from simulations.
