Dynamics of dilute gases: a statistical approach

  • Thierry Bodineau

    CNRS, Ecole Polytechnique, Institut Polytechnique de Paris, Palaiseau, France
  • Isabelle Gallagher

    Ecole Normale Supérieure, Paris, France
  • Laure Saint-Raymond

    IHES, Bures sur Yvette, France
  • Sergio Simonella

    Ecole Normale Supérieure de Lyon, CNRS, Lyon, France
Dynamics of dilute gases: a statistical approach cover
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The evolution of a gas can be described by different models depending on the observation scale. A natural question, raised by Hilbert in his sixth problem, is whether these models provide consistent predictions. In particular, for rarefied gases, it is expected that continuum laws of kinetic theory can be obtained directly from molecular dynamics governed by the fundamental principles of mechanics.

In the case of hard sphere gases, Lanford (1975) showed that the Boltzmann equation emerges as the law of large numbers in the low density limit, at least for very short times. The goal of this survey is to present recent progress in the understanding of this limiting process, providing a complete statistical description.