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

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 $V_infty$ and prove that, under suitable smallness assumptions, the approach to equilibrium is begin{displaymath}vert V(t)-V_inftyvertapprox frac{C}{t^{d+1}}, end{displaymath} 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.