Weak-strong uniqueness for fluid-rigid body interaction problem with slip boundary condition

TL;DR

This paper proves that, for a fluid-rigid body interaction with slip boundary conditions, the unique strong solution is also unique among weak solutions, establishing a fundamental weak-strong uniqueness result in fluid-structure interaction with moving boundaries.

Contribution

It presents the first weak-strong uniqueness theorem for fluid-structure interaction problems involving a moving boundary with slip boundary conditions.

Findings

Weak-strong uniqueness established for fluid-rigid body system

First such result with Navier slip boundary condition

Enhances understanding of solution behavior in fluid-structure interactions

Abstract

We consider a coupled PDE-ODE system describing the motion of the rigid body in a container filled with the incompressible, viscous fluid. The fluid and the rigid body are coupled via Navier slip boundary condition. We prove that the local in time strong solution is unique in the larger class of weak solutions on the interval of its existence. This is the first weak-strong uniqueness result in the area of fluid-structure interaction with a moving boundary.