no. 2
On the motion of a body in thermal equilibrium immersed in a perfect gas
ESAIM: Modélisation mathématique et analyse numérique, Tome 42 (2008) no. 2, pp. 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(t) to the limiting velocity V ∞ and prove that, under suitable smallness assumptions, the approach to equilibrium is

|V(t)-V ∞ |≈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 : 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 
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     title = {On the motion of a body in thermal equilibrium immersed in a perfect gas},
     journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
     pages = {263--275},
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Aoki, Kazuo; Cavallaro, Guido; Marchioro, Carlo; Pulvirenti, Mario. On the motion of a body in thermal equilibrium immersed in a perfect gas. ESAIM: Modélisation mathématique et analyse numérique, Tome 42 (2008) no. 2, pp. 263-275. doi: 10.1051/m2an:2008007

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