Comptes Rendus
no. 7-8
Mathematical Physics
The Boltzmann–Grad limit of the periodic Lorentz gas in two space dimensions
[La limite de Boltzmann–Grad du gaz de Lorentz périodique en dimension deux d'espace]

Présenté par : Pierre-Louis Lions

Emanuele Caglioti1 ; François Golse2
1 Università di Roma “La Sapienza”, Dipartimento di Matematica “Guido Castelnuovo”, P.le Aldo Moro 2, 00185 Rome, Italy
2 École polytechnique, centre de mathématiques Laurent-Schwartz, 91128 Palaiseau cedex, France
Comptes Rendus. Mathématique, Volume 346 (2008) no. 7-8, pp. 477-482.

Le gaz de Lorentz périodique est le système dynamique correspondant au mouvement libre dans le plan d'une particule ponctuelle rebondissant de manière élastique sur un système de disques de rayon r centrés aux points de coordonnées entières. On étudie ce mouvement pour r→0+ sur des temps de l'ordre de 1/r.

The periodic Lorentz gas is the dynamical system corresponding to the free motion of a point particle in a periodic system of fixed spherical obstacles of radius r centered at the integer points of the Euclidian plane, assuming all collisions of the particle with the obstacles to be elastic. In this Note, we study this motion on time intervals of order 1/r as r→0+.

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DOI : 10.1016/j.crma.2008.01.016
Emanuele Caglioti 1 ; François Golse 2

1 Università di Roma “La Sapienza”, Dipartimento di Matematica “Guido Castelnuovo”, P.le Aldo Moro 2, 00185 Rome, Italy
2 École polytechnique, centre de mathématiques Laurent-Schwartz, 91128 Palaiseau cedex, France 
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Emanuele Caglioti; François Golse. The Boltzmann–Grad limit of the periodic Lorentz gas in two space dimensions. Comptes Rendus. Mathématique, Volume 346 (2008) no. 7-8, pp. 477-482. doi : 10.1016/j.crma.2008.01.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.01.016/

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