Archive for Rational Mechanics and Analysis

, Volume 179, Issue 2, pp 153–216 | Cite as

The Reconstruction Problem for the Euler-Poisson System in Cosmology

  • Grégoire Loeper


The motion of a continuum of matter subject to gravitational interaction is classically described by the Euler-Poisson system. Prescribing the density of matter at initial and final times, we are able to obtain weak solutions for this equation 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. Then we see that such minimizing solutions are consistent with smooth solutions of the Euler-Poisson system and enjoy some special regularity properties.


Neural Network Transportation Complex System Weak Solution Nonlinear Dynamics 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  1. 1.EPFL, SB-IMBLausanne

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