On the motion of a rigid body in a two-dimensional irregular ideal flow

TL;DR

This paper proves that a rigid body's trajectory in a two-dimensional ideal flow with bounded vorticity is Gevrey if the body's boundary is Gevrey, extending previous results to irregular flows.

Contribution

It extends prior work by showing Gevrey regularity of the body's trajectory in irregular ideal flows with bounded vorticity.

Findings

The body's trajectory is Gevrey if the boundary is Gevrey.

Existence and uniqueness of solutions are established for the flow with bounded vorticity.

The result generalizes previous work to irregular flow cases.

Abstract

We consider the motion of a rigid body immersed in an ideal flow occupying the plane, with bounded initial vorticity. In that case there exists a unique corresponding solution which is global in time, in the spirit of the famous work by Yudovich for the fluid alone. We prove that if the body's boundary is Gevrey then the body's trajectory is Gevrey. This extends the previous work [Glass-Sueur-Takahashi, 2011] to a case where the flow is irregular.