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Thierry Bodineau; Isabelle Gallagher; Laure Saint-Raymond; Sergio Simonella
One-sided convergence in the Boltzmann–Grad limit
Annales de la faculté des sciences de Toulouse Sér. 6, 27 no. 5 (2018), p. 985-1022, doi: 10.5802/afst.1589
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Résumé - Abstract

Ce papier présente diverses contributions basées sur le travail fondamental de Lanford [21] qui a permis d’obtenir l’équation de Boltzmann à partir de la dynamique (réversible) des sphères dures dans la limite de densité faible.

On s’intéresse en particulier aux hypothèses sur la donnée initiale et sur la façon dont elles codent l’irréversibilité. On montre que l’impossibilité de renverser le sens du temps dans l’équation de Boltzmann (qui est exprimée notamment dans le théorème H) est liée à l’absence de convergence des marginales d’ordre supérieur sur des ensembles singuliers. Un contre exemple explicite permet de caractériser les ensembles, de mesure asymptotiquement nulle, où la donnée initiale doit converger pour obtenir la dynamique de Boltzmann.

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