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

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 à la Delort in a particular case. These solutions satisfy the energy inequality and the body acceleration is bounded.

References in corpus (1)

• A Kato type Theorem for the inviscid limit of the Navier-Stokes equations with a moving rigid body

Cited by in corpus (4)

• Uniqueness of Yudovich's solutions to the 2D incompressible Euler equation despite the presence of sources and sinks
• Motion of a particle immersed in a two dimensional incompressible perfect fluid and point vortex dynamics
• Existence of weak solutions to the two-dimensional incompressible Euler equations in the presence of sources and sinks
• Measure-valued solutions and weak-strong uniqueness for the incompressible inviscid fluid-rigid body interaction