On the motion of a rigid body in a two-dimensional ideal flow with vortex sheet initial data

TL;DR

This paper extends Delort's existence results for 2D incompressible Euler equations to include a moving rigid body with vortex sheet initial data, ensuring bounded acceleration and energy conservation.

Contribution

It proves the existence of weak solutions for a rigid body in a 2D ideal flow with vortex sheet initial data, satisfying energy and bounded acceleration conditions.

Findings

Existence of weak solutions with vortex sheet initial data

Solutions satisfy energy inequality

Rigid body acceleration remains bounded

Abstract

A famous result by Delort about the two-dimensional incompressible Euler equations is the existence of weak solutions when the initial vorticity is a diffuse bounded Radon measure with distinguished sign. In this paper we are interested in the case where there is a rigid body immersed in the fluid moving under the action of the fluid pressure. We succeed to prove the existence of solutions \`a la Delort in a particular case. These solutions satisfy the energy inequality and the body acceleration is bounded.