Motion of a rigid body in a compressible Fluid with Navier-slip boundary condition

TL;DR

This paper presents the first mathematical analysis of a compressible fluid-rigid body system with Navier-slip boundary conditions, proving the existence of weak solutions up to collision.

Contribution

It introduces a novel analysis of a compressible fluid-rigid body system with Navier-slip boundary conditions, establishing existence results.

Findings

Existence of weak solutions up to collision

First mathematical analysis with Navier-slip conditions

Framework for future studies on fluid-structure interactions

Abstract

In this work, we study the motion of a rigid body in a bounded domain which is filled with a compressible isentropic fluid. We consider the Navier-slip boundary condition at the interface as well as at the boundary of the domain. This is the first mathematical analysis of a compressible fluid-rigid body system where Navier-slip boundary conditions are considered. We prove existence of a weak solution of the fluid-structure system up to collision.