Open AccessFrom classical mechanics to kinetic theory and fluid dynamics
Author(s) -
Isabelle Gallagher
Publication year - 2014
Publication title -
journées équations aux dérivées partielles
Language(s) - English
Resource type - Journals
eISSN - 2118-9366
pISSN - 0752-0360
DOI - 10.5802/jedp.105
Subject(s) - kinetic theory , kinetic energy , boltzmann equation , infinity , hard spheres , classical mechanics , physics , work (physics) , boltzmann constant , zero (linguistics) , radius , mathematical physics , theoretical physics , mathematics , mathematical analysis , computer science , quantum mechanics , philosophy , linguistics , computer security
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.
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