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

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 $\mathbb{R}^{2}$. We prove the existence of global-in-time weak solutions with constant non-zero circulation at infinity.