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We consider the evolution of a small rigid body in an incompressible viscousfluid filling the whole space $\rline^3$. When the small rigid body shrinks toa "massless" point in the sense that its density is constant, we prove that thesolution of the fluid-rigid body system converges to a solution of theNavier-Stokes equations in the full space. Based on some $L^p-L^q$ estimates ofthe fluid-structure semigroup and a fixed point argument, we obtain a uniformestimate of velocity of the rigid body. This allows us to construct admissibletest functions which plays a key role in the procedure of passing to the limit.

The vanishing limit of a rigid body in three-dimensional viscous incompressible fluid