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

We consider a convex body in the whole space, 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)| behaves like 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 in which for simplicity the body was assumed to be a disk.