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 power-law, like t^(-d-1), where d is the dimension of the space. This approach is not exponential, as typical in friction problems, and even slower than for the same problem with elastic collisions.
On the motion of a body in thermal equilibrium immersed in a perfect gas / Kazuo, Aoki; Cavallaro, Guido; Marchioro, Carlo; Pulvirenti, Mario. - In: MODÉLISATION MATHÉMATIQUE ET ANALYSE NUMÉRIQUE. - ISSN 0764-583X. - STAMPA. - 42:2(2008), pp. 263-275. [10.1051/m2an:2008007]