Self-propelled motion of a rigid body inside a density dependent incompressible fluid

TL;DR

This paper proves the global existence of weak solutions for a model describing a self-propelled rigid body moving within a density-dependent incompressible fluid, considering slip at the interface.

Contribution

It establishes the existence of weak solutions for a complex fluid-structure interaction system with density variation and slip boundary conditions.

Findings

Proves global existence of weak solutions.

Handles density-dependent incompressible Navier-Stokes system.

Incorporates slip boundary conditions at the fluid-solid interface.

Abstract

This paper is devoted to the existence of a weak solution to a system describing a self-propelled motion of a rigid body in a viscous fluid in the whole $\mathbb{R}^3$. The fluid is modelled by the incompressible nonhomogeneous Navier-Stokes system with a nonnegative density. The motion of the rigid body is described by the balance of linear and angular momentum. We consider the case where slip is allowed at the fluid-solid interface through Navier condition and prove the global existence of a weak solution.