The reconstruction problem for the Euler-Poisson system in cosmology (Q816945)

The Euler-Poisson system describes the motion of a self-gravitating fluid. It is used in cosmology to model the evolution of the primitive universe. The so-called reconstruction problem looks for the intermediate states of the universe, as well as the initial and present velocities. The problem amounts to reconstructing a solution of the Euler-Poisson system based on the knowledge of the initial and final density fields, and seems ill-posed. The authors are able to obtain weak solutions by minimizing the action of the Lagrangian which is a convex functional. Through this variational formulation, the reconstruction problem becomes very similar to an optimal transportation problem.