Archive for Rational Mechanics and Analysis

, Volume 152, Issue 4, pp 327–355 | Cite as

Entropy Dissipation and Long-Range Interactions

  • R. Alexandre
  • L. Desvillettes
  • C. Villani
  • B. Wennberg

Abstract:

We study Boltzmann's collision operator for long-range interactions, i.e., without Grad's angular cut-off assumption. We establish a functional inequality showing that the entropy dissipation controls smoothness of the distribution function, in a precise sense. Our estimate is optimal, and gives a unified treatment of both the linear and the nonlinear cases. We also give simple and self-contained proofs of several useful results that were scattered in previous works. As an application, we obtain several helpful estimates for the Cauchy problem, and for the Landau approximation in plasma physics.

Keywords

Entropy Distribution Function Cauchy Problem Plasma Physic Unify Treatment 
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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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • R. Alexandre
    • 1
  • L. Desvillettes
    • 2
  • C. Villani
    • 3
  • B. Wennberg
    • 4
  1. 1.MAPMO, Université d'Orléans¶B.P. 6759, 45067 Orléans Cedex 2¶France¶e-mail{Alexandre.Radja@labomath.univ-orleans.frFR
  2. 2.Ecole Normale Supérieure de Cachan¶Centre de Mathématiques et Leurs Applications¶61 Avenue du Président Wilson¶94235 Cachan, France¶e-mail: desville@cmla.ens-cachan.frFR
  3. 3.École Normale Supérieure, DMA¶45 rue d'Ulm, 75230 Paris Cedex 05, France¶e-mail: villani@dma.ens.frFR
  4. 4.Department of Mathematics, Chalmers University of Technology¶ 541296 Göteborg, Sweden¶e-mail: wennberg@math.chalmers.seSE

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