The steady problem of the motion of a rigid ball in a Stokes-Poiseuille flow: differentiability of the solution with respect to the ball position

摘要

This paper deals with the steady problem of the motionof a rigid body in a viscous incompressible fluid that fills a cylindricaldomain. The fluid flow is governed by the Stokes equation and tends toPoiseuille flow at infinity. The body is a ball that moves according to thelaws of classical mechanics. The unique solvability of this problem wasproved in an earlier work of the authors. Here, the differentiability of thesolution in the function space L2 with respect to the position of the ballis established.