On the motion of a convex body interacting with a perfect gas in the mean-field approximation

Abstract

We consider a convex body in R^3, moving along the x-axis, immersed in an infinitely extended perfect gas in the mean-field approximation. We assume that the gas particles interact with the body by means of elastic collisions. Giving to the body an initial velocity V_0, we prove that, for |V_0| small enough, |V (t)| ≈ C t^{−5} for large t, being C a positive constant depending on the medium and on the shape of the obstacle. The power law approach to the equilibrium V = 0, instead of the exponential one (typical in viscous friction problems), is due to the long memory effect of the recollisions. This paper completes the analysis made in previous papers (see [7] and [8]), in which for simplicity the body was assumed to be a disk.

Keywords

• viscous friction
• microscopic dynamics
• dynamics with memory