On the Velocity of a Small Rigid Body in a Viscous Incompressible Fluid in Dimension Two and Three

In this paper we study the evolution of a small rigid body in a viscous incompressible fluid, in particular we show that a small particle is not accelerated by the fluid in the limit when its size converges to zero under a lower bound on its mass. This result is based on a new a priori estimate on the velocities of the centers of mass of rigid bodies that holds in the case when their masses are also allowed to decrease to zero.

Automated summary

In this paper, the evolution of a small rigid body in a viscous incompressible fluid is studied. It is shown that a small particle is not accelerated by the fluid as its size approaches zero under a lower bound on its mass. This result is based on a new a priori estimate on the velocities of the centers of mass of rigid bodies, even when their masses are allowed to decrease to zero.