In these notes we report on a work in collaboration with Thierry Bodineau and Laure Saint-Raymond, where we show how the heat equation can be obtained from a deterministic system of hard spheres when the number of particles goes to infinity while their radius simultaneously goes to zero. As suggested by Hilbert in his sixth problem, the kinetic theory of Boltzmann is used as an intermediate level of description.
@incollection{JEDP_2014____A2_0,
author = {Gallagher, Isabelle},
title = {From classical mechanics to kinetic theory and fluid dynamics},
booktitle = {},
series = {Journ\'ees \'equations aux d\'eriv\'ees partielles},
eid = {2},
pages = {1--14},
publisher = {Groupement de recherche 2434 du CNRS},
year = {2014},
doi = {10.5802/jedp.105},
language = {en},
url = {http://www.numdam.org/articles/10.5802/jedp.105/}
}
TY - JOUR AU - Gallagher, Isabelle TI - From classical mechanics to kinetic theory and fluid dynamics JO - Journées équations aux dérivées partielles PY - 2014 SP - 1 EP - 14 PB - Groupement de recherche 2434 du CNRS UR - http://www.numdam.org/articles/10.5802/jedp.105/ DO - 10.5802/jedp.105 LA - en ID - JEDP_2014____A2_0 ER -
%0 Journal Article %A Gallagher, Isabelle %T From classical mechanics to kinetic theory and fluid dynamics %J Journées équations aux dérivées partielles %D 2014 %P 1-14 %I Groupement de recherche 2434 du CNRS %U http://www.numdam.org/articles/10.5802/jedp.105/ %R 10.5802/jedp.105 %G en %F JEDP_2014____A2_0
Gallagher, Isabelle. From classical mechanics to kinetic theory and fluid dynamics. Journées équations aux dérivées partielles (2014), article no. 2, 14 p. doi : 10.5802/jedp.105. http://www.numdam.org/articles/10.5802/jedp.105/
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