The Inverse Problem for the Euler-Poisson system in Cosmology

Details The Inverse Problem for the Euler-Poisson system in Cosmology The Inverse Problem for the Euler-Poisson system in Cosmology

2003-06-30

arxiv.org/abs/math/0306430v2

Mathematics

Analysis of PDEs

40 pages

Scientific paper

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. Then we see that such minimizing solutions are consistent with smooth solutions of the Euler-Poisson system and enjoy some special regularity properties. Meanwhile some intersting links with with Hamilton-Jacobi equations are found.

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