Low regularity solutions for the two-dimensional "rigid body + incompressible Euler" system

TL;DR

This paper proves the global existence of solutions for a 2D incompressible fluid with a moving solid body, even with low regularity initial vorticity and without finite energy assumptions.

Contribution

It establishes global solutions for the 2D rigid body-incompressible Euler system with low regularity initial vorticity, extending previous results to less regular initial data.

Findings

Global existence of solutions for initial vorticity in L^p, p>1

Solutions do not require finite energy

Initial vorticity is compactly supported

Abstract

In this note we consider the motion of a solid body in a two dimensional incompressible perfect fluid. We prove the global existence of solutions in the case where the initial vorticity belongs to $L^p$ with $p>1$ and is compactly supported. We do not assume that the energy is finite.