A small solid body with large density in a planar fluid is negligible

Abstract

In this article, we consider a small rigid body moving in a viscous fluid filling the whole plane. We assume that the diameter of the rigid body goes to 0, that the initial velocity has bounded energy and that the density of the rigid body goes to infinity. We prove that the rigid body has no influence on the limit equation by showing convergence of the solutions towards a solution of the Navier-Stokes equations in the full plane.