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Article Dans Une Revue Physica A: Statistical Mechanics and its Applications Année : 2004

Chapman-Enskog derivation of the generalized Smoluchowski equation

Résumé

We use the Chapman-Enskog method to derive the Smoluchowski equation from the Kramers equation in a high friction limit. We consider two main extensions of this problem: we take into account a uniform rotation of the background medium and we consider a generalized class of Kramers equations associated with generalized free energy functionals. We mention applications of these results to systems with long-range interactions (self-gravitating systems, 2D vortices, bacterial populations,...). In that case, the Smoluchowski equation is non-local. In the limit of short-range interactions, it reduces to a generalized form of the Cahn-Hilliard equation. These equations are associated with an effective generalized thermodynamical formalism.

Dates et versions

hal-00139219 , version 1 (29-03-2007)

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Pierre-Henri Chavanis, Philippe Laurencot, Mohammed Lemou. Chapman-Enskog derivation of the generalized Smoluchowski equation. Physica A: Statistical Mechanics and its Applications, 2004, 341, pp.145-164. ⟨10.1016/j.physa.2004.04.102⟩. ⟨hal-00139219⟩
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