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Chapman–Enskog derivation of the generalized Smoluchowski equation

Author

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  • Chavanis, Pierre-Henri
  • Laurençot, Philippe
  • Lemou, Mohammed

Abstract

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, etc.). 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.

Suggested Citation

  • Chavanis, Pierre-Henri & Laurençot, Philippe & Lemou, Mohammed, 2004. "Chapman–Enskog derivation of the generalized Smoluchowski equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 341(C), pages 145-164.
    • Handle: RePEc:eee:phsmap:v:341:y:2004:i:c:p:145-164
    DOI: 10.1016/j.physa.2004.04.102
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