  The generally held view that a model of large-scale structure, formed by
collisionless matter in the Universe, can be based on the matter model ``dust''
fails in the presence of multi-stream flow, i.e., velocity dispersion. We argue
that models for large-scale structure should rather be constructed for a flow
which describes the average motion of a multi-stream system. We present a
clearcut reasoning how to approach the problem and derive an evolution equation
for the mean peculiar-velocity relative to background solutions of
Friedmann-Lema\^\i tre type. We consider restrictions of the nonlinear problem
and show that the effect of velocity dispersion gives rise to an effective
viscosity of non-dissipative gravitational origin. We discuss subcases which
arise naturally from this approach: the ``sticky particle model'' and the
``adhesion approximation''. We also construct a novel approximation that
features adhesive action in the multi-stream regime while conserving momentum,
which was considered a drawback of the standard approximation based on Burger's
equation. We finally argue that the assumptions made to obtain these models
should be relaxed and we discuss how this can be achieved.
