On the 2D `viscous incompressible fluid + rigid body' system with Navier conditions and unbounded energy

TL;DR

This paper studies the motion of a rigid body in a 2D viscous incompressible fluid with Navier slip boundary conditions, proving the existence of global weak solutions with non-zero circulation in an unbounded domain.

Contribution

It establishes the existence of global weak solutions for the 2D viscous fluid and rigid body system with Navier boundary conditions in an unbounded domain.

Findings

Existence of global weak solutions with non-zero circulation.

Analysis in the full plane $ ^2$ setting.

Application of Navier slip conditions on the body's boundary.

Abstract

In this paper we consider the motion of a rigid body in a viscous incompressible fluid when some Navier slip conditions are prescribed on the body's boundary. The whole `viscous incompressible fluid + rigid body' system is assumed to occupy the full plane $\R^{2}$. We prove the existence of global-in-time weak solutions with constant non-zero circulation at infinity.