On the Periodic Lorentz Gas and the Lorentz Kinetic Equation

François Golse (1, 2)

1 CMLS - Centre de Mathématiques Laurent Schwartz
2 LJLL - Laboratoire Jacques-Louis Lions

We prove that the Boltzmann-Grad limit of the Lorentz gas with periodic distribution of scatterers cannot be described with a linear Boltzmann equation. This is at variance with the case of a Poisson distribution of scatterers, for which the convergence to the linear Boltzmann equation has been proved by Gallavotti [Phys. Rev. (2) 185 (1969), p. 308].

Mots clés: Lorentz gas; Sinai billiards; Kinetic theory; Boltzmann-Grad limit

Domaines: Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]; Physique mathématique [math-ph]; Systèmes dynamiques [math.DS]

François Golse. On the Periodic Lorentz Gas and the Lorentz Kinetic Equation. Annales de la Faculté des Sciences de Toulouse. Mathématiques., 2008, 17 (4), pp.735-749. ⟨hal-00138843⟩