  We consider exact solutions to the problem of ballistic aggregation in a flow
of adhesive particles, providing a model for large-scale structure formation in
cosmology within the framework of the Zel'dovich approximation. Two different
explicit variational constructions, suggested for this problem by (A.
Shnirelman, 1986) and (E Weinan et al, 1996) in the case of flat symmetry, are
shown to be equivalent. Explicit solutions are constructed for flows of
cylindric and spherical symmetry. Two explicit counterexamples, showing that
natural generalizations of both variational constructions fail to provide
solutions for nonsymmetric multidimensional flows, are presented.
