Free access article

ESAIM: M2AN 42 (2008) 263-275
DOI: 10.1051/m2an:2008007

On the motion of a body in thermal equilibrium immersed in a perfect gas

Kazuo Aoki¹, Guido Cavallaro², Carlo Marchioro² and Mario Pulvirenti<sup>2

1</sup>  Department of Mechanical Engineering and Science and Advanced Research Institute of Fluid Science and Engineering, Graduate School of Engineering, Kyoto University, Kyoto 606-8501, Japan. aoki@aero.mbox.media.kyoto-u.ac.jp
²  Dipartimento di Matematica, Università di Roma "La Sapienza", Piazzale A. Moro 2, 00185, Roma, Italy. cavallar@mat.uniroma1.it; marchior@mat.uniroma1.it; pulvirenti@mat.uniroma1.it

(Received March 31, 2007. Revised October 16, 2007. Published online 27 March 2008.)

Abstract
We consider a body immersed in a perfect gas and moving under the action of a constant force. Body and gas are in thermal equilibrium. We assume a stochastic interaction body/medium: when a particle of the medium hits the body, it is absorbed and immediately re-emitted with a Maxwellian distribution. This system gives rise to a microscopic model of friction. We study the approach of the body velocity V(t) to the limiting velocity and prove that, under suitable smallness assumptions, the approach to equilibrium is

where d is the dimension of the space, and C is a positive constant. This approach is not exponential, as typical in friction problems, and even slower than for the same problem with elastic collisions.

Mathematics Subject Classification. 76P05, 82B40, 82C40, 35L45, 35L50

Key words: Kinetic theory of gases, Boltzmann equation, free molecular gas, friction problem, approach to equilibrium.


© EDP Sciences, SMAI 2008