  A hydrodynamic formulation of the evolution of large-scale structure in the
Universe is presented. It relies on the spatially coarse-grained description of
the dynamical evolution of a many-body gravitating system. Because of the
assumed irrelevance of short-range (``collisional'') interactions, the way to
tackle the hydrodynamic equations is essentially different from the usual case.
The main assumption is that the influence of the small scales over the
large-scale evolution is weak: this idea is implemented in the form of a
large-scale expansion for the coarse-grained equations. This expansion builds a
framework in which to derive in a controlled manner the popular ``dust'' model
(as the lowest-order term) and the ``adhesion'' model (as the first-order
correction). It provides a clear physical interpretation of the assumptions
involved in these models and also the possibility to improve over them.
