| Abstract: |
| The adhesion model is a multidimensional model of mass transport in cosmology in a perturbed Einstein-de Sitter universe, which reduces to sticky particle flow in 1D. Velocity is given by a Hopf-Lax formula and concentrates mass on sheets, filaments and points, but it is known that momentum is not conserved in general. Work in the astronomy literature by Brenier, Frisch and collaborators relates the problem of reconstructing the primeval velocity distribution to an optimal mass transport problem. We carry out a mathematical analysis of the initial value problem, establishing a number of basic facts, including the uniqueness of a `sticky` mass flow and a characterization of its absolutely continuous part in terms of a natural Monge-Amp\`ere equation. We find that the singular part is not necessarily determined correctly by optimal transport, and this can result in inexact reconstruction. |
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