One-sided convergence in the Boltzmann-Grad limitReport as inadecuate

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1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique 2 IMJ - Institut de Mathématiques de Jussieu 3 DMA - Département de Mathématiques et Applications 4 Zentrum Mathematik, M5 Technische Universität München

Abstract : We review various contributions on the fundamental work of Lanford deriving the Boltzmann equation from hard-sphere dynamics in the low density limit. We focus especially on the assumptions made on the initial data and on how they encode irreversibility. The impossibility to reverse time in the Boltzmann equation expressed for instance by Boltzmann-s H-theorem is related to the lack of convergence of higher order marginals on some singular sets. Explicit counterexamples single out the microscopic sets where the initial data should converge in order to produce the Boltzmann dynamics.

Keywords : Boltzmann equat

Author: Thierry Bodineau - Isabelle Gallagher - Laure Saint-Raymond - Sergio Simonella -



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