Article

Archive for Rational Mechanics and Analysis

, Volume 115, Issue 4, pp 297-310

First online:

On the connection between Hamiltonian many-particle systems and the hydrodynamical equations

  • Karl OelschlägerAffiliated withInstitut für Angewandte Mathematik, Universität Heidelberg

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Summary

We consider certain Hamiltonian systems with many particles interacting through a potential whose range is large in comparison with the typical distance between neighbouring particles. It is shown that the empirical processes of the positions and the velocities respectively converge to solutions of the continuity equation and the Euler equation, in the limit as the particle number tends to infinity.