The evolution of a gas can be described by different models depending on the obser- vation 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 [46] 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.
DYNAMICS OF DILUTE GASES : A STATISTICAL APPROACH / Bodineau, Thierry; Gallagher, Isabelle; Saint-Raymond, Laure; Simonella, Sergio. - (2023). (Intervento presentato al convegno International Congress of Mathematicians tenutosi a virtual event).
DYNAMICS OF DILUTE GASES : A STATISTICAL APPROACH
Thierry Bodineau;Isabelle Gallagher;Sergio Simonella
2023
Abstract
The evolution of a gas can be described by different models depending on the obser- vation 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 [46] 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
