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In this paper we study the evolution of a small rigid body in a viscousincompressible fluid, in particular we show that a small particle is notaccelerated by the fluid in the limit when its size converges to zero under alower bound on its mass. This result is based on a new a priori estimate on thevelocities of the centers of mass of rigid bodies that holds in the case whentheir masses are also allowed to decrease to zero.

On the velocity of a small rigid body in a viscous incompressible fluid in dimension two and three