# On the small rigid body limit in 3D incompressible flows

## TL;DR

This paper proves that as a small rigid body's size shrinks and its density increases, the coupled fluid-rigid body system's solution converges to the standard Navier-Stokes solution in an unbounded domain.

## Contribution

It establishes the rigorous limit process for a shrinking, dense rigid body in a viscous incompressible fluid, connecting coupled and pure fluid models.

## Key findings

- Solution converges to Navier-Stokes equations without rigid body
- Rigorous mathematical proof of the small rigid body limit
- Demonstrates the effect of vanishing size and increasing density

## Abstract

We consider the evolution of a small rigid body in an incompressible viscous fluid filling the whole space. The motion of the fluid is modelled by the Navier-Stokes equations, whereas the motion of the rigid body is described by the conservation law of linear and angular momentum. Under the assumption that the diameter of the rigid body tends to zero and that the density of the rigid body goes to infinity, we prove that the solution of the fluid-rigid body system converges to a solution of the Navier-Stokes equations in the full space without rigid body.