Wall effect on the motion of a rigid body immersed in a free molecular flow

Abstract

Motion of a rigid body immersed in a semi-infinite expanse of free molecular gas in a d-dimensional region bounded by an infinite plane wall is studied. The free molecular flow is described by the free Vlasov equation with the specular boundary condition. We show that the velocity V (t) of the body approaches its terminal velocity V1 according to a power law V ∞ - V (t) ≈ t-(d-1) by carefully analyzing the pre-collisions due to the presence of the wall. The exponent d-1 is smaller than d+2 for the case without the wall found in the classical work by Caprino, Marchioro and Pulvirenti [Comm. Math. Phys., 264 (2006), 167{189] and thus slower convergence results from the presence of the wall.