| Issue |
ESAIM: M2AN
Volume 42, Number 2, March-April 2008
|
|
|---|---|---|
| Page(s) | 263 - 275 | |
| DOI | https://doi.org/10.1051/m2an:2008007 | |
| Published online | 27 March 2008 | |
On the motion of a body in thermal equilibrium immersed in a perfect gas
1
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:
31
March
2007
Revised:
16
October
2007
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
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