On the motion of a body in thermal equilibrium immersed in a perfect gas
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 42 (2008) no. 2, p. 263-275

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 $V\left(t\right)$ to the limiting velocity ${V}_{\infty }$ and prove that, under suitable smallness assumptions, the approach to equilibrium is $|V\left(t\right)-{V}_{\infty }|\approx \frac{C}{{t}^{d+1}},$ 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.

DOI : https://doi.org/10.1051/m2an:2008007
Classification:  76P05,  82B40,  82C40,  35L45,  35L50
Keywords: kinetic theory of gases, Boltzmann equation, free molecular gas, friction problem, approach to equilibrium
@article{M2AN_2008__42_2_263_0,
author = {Aoki, Kazuo and Cavallaro, Guido and Marchioro, Carlo and Pulvirenti, Mario},
title = {On the motion of a body in thermal equilibrium immersed in a perfect gas},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis - Mod\'elisation Math\'ematique et Analyse Num\'erique},
publisher = {EDP-Sciences},
volume = {42},
number = {2},
year = {2008},
pages = {263-275},
doi = {10.1051/m2an:2008007},
zbl = {1133.76046},
mrnumber = {2405148},
language = {en},
url = {http://www.numdam.org/item/M2AN_2008__42_2_263_0}
}

Aoki, Kazuo; Cavallaro, Guido; Marchioro, Carlo; Pulvirenti, Mario. On the motion of a body in thermal equilibrium immersed in a perfect gas. ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique, Volume 42 (2008) no. 2, pp. 263-275. doi : 10.1051/m2an:2008007. http://www.numdam.org/item/M2AN_2008__42_2_263_0/

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