The motion of a rigid body and a viscous fluid in a bounded domain in presence of collisions

TL;DR

This paper proves the global existence of weak solutions for the motion of a rigid body in a viscous fluid within a bounded domain, allowing for collisions with the boundary, governed by Navier-Stokes equations.

Contribution

It establishes the first global in time weak solution existence result for a rigid body in a viscous fluid with boundary collisions under Navier boundary conditions.

Findings

Global weak solutions exist for the system

Collisions with the boundary are permitted in the model

The results apply to Navier boundary conditions

Abstract

We consider the motion of a rigid body, governed by the Navier-Stokes equations in a bounded domain. Navier's condition is prescribed on the boundary of the body. We give the global in a time solvability result of weak solution. The result permits a possibility of collisions of the body with the boundary of the domain.