A small rigid body immersed in a three-dimensional viscous fluid and the vanishing viscosity limit

In this paper, we investigate the asymptotic behavior of a coupled fluid–rigid body system, consisting of a rigid body immersed in a three-dimensional viscous incompressible fluid, as the body size and the fluid viscosity vanish. We prove that the limiting velocity field is governed by the whole-space incompressible Euler equations. Moreover, the influence of the fluid on the rigid body motion is shown to vanish in this limit.