On the motion of a small light body immersed in a two dimensional incompressible perfect fluid with vorticity

TL;DR

This paper proves that as a small rigid body shrinks to a point in a 2D incompressible perfect fluid with vorticity, the combined system converges to the vortex-wave system, extending previous results to the massless case in unbounded domains.

Contribution

It establishes the convergence of the fluid-rigid body system to the vortex-wave system for a shrinking massless body in an unbounded domain, extending prior work to this new setting.

Findings

Convergence of the system to the vortex-wave model as the body shrinks.

Extension of previous results to unbounded domains with vorticity.

Demonstration of the massless limit in a 2D incompressible fluid.

Abstract

In this paper we consider the motion of a rigid body immersed in a two dimensional unbounded incompressible perfect fluid with vorticity. We prove that when the body shrinks to a massless pointwise particle with fixed circulation, the "fluid+rigid body" system converges to the vortex-wave system introduced by Marchioro and Pulvirenti in [11]. This extends both the paper [2] where the case of a solid tending to a massive pointwise particle was tackled and the paper [3] where the massless case was considered but in a bounded cavity filled with an irrotational fluid.