# American Institute of Mathematical Sciences

June  2010, 3(2): 281-297. doi: 10.3934/krm.2010.3.281

## Rigorous validity of the Boltzmann equation for a thin layer of a rarefied gas

 1 Dipartimento di Matematica pura ed Applicata, Università dell’Aquila, Via Vetoio - Coppito, L’Aquila, 67100, Italy 2 Dipartimento di Matematica Guido Castelnuovo, Università La Sapienza, P.e Aldo Moro, 2, 67100 Roma, Italy

Received  January 2010 Revised  February 2010 Published  May 2010

We consider a thin layer of a rarified gas modeled by a large hard-sphere system and show that, as long as the thickness of the layer is much larger than the interaction length, the limiting behavior is described, at least for short times, by a Boltzmann equation with two-dimensional position variable and three-dimensional velocity. By the analysis of the Lorentz gas we argue that, if the thickness of the layer is of the same order of the interaction length, this is not the case.
Citation: Raffaele Esposito, Mario Pulvirenti. Rigorous validity of the Boltzmann equation for a thin layer of a rarefied gas. Kinetic & Related Models, 2010, 3 (2) : 281-297. doi: 10.3934/krm.2010.3.281
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