  This work reports on the application of the Eulerian perturbation theory to a
recently proposed model of cosmological structure formation by gravitational
instability (astro-ph/0009414). Its physical meaning is discussed in detail and
put in perspective of previous works. The model incorporates in a systematic
fashion corrections to the popular dust model due to multistreaming and, more
generally, the small-scale, virialized degrees of freedom. It features a
time-dependent length scale L(t) estimated to be L/r0 ~ 0.1 (r0(t) is the
nonlinear scale, at which the density variance =1). The model provides a new
angle on the dust model and allows to overcome some of its limitations. Thus,
the scale L(t) works as a physically meaningful short-distance cutoff for the
divergences appearing in the perturbation expansion of the dust model when
there is too much initial power on small scales. The model also incorporates
the generation of vorticity by tidal forces; according to the perturbational
result, the filtered vorticity for standard CDM initial conditions should be
significant today only at scales below ~ 1 Mpc/h.
