Measure-valued solutions and weak-strong uniqueness for the incompressible inviscid fluid-rigid body interaction

TL;DR

This paper establishes the existence of measure-valued solutions for an inviscid fluid-rigid body interaction system and proves their uniqueness when a strong solution exists, advancing understanding of such coupled PDE-ODE models.

Contribution

It introduces measure-valued solutions for the inviscid fluid-rigid body system and demonstrates weak-strong uniqueness, linking these solutions to classical solutions under certain conditions.

Findings

Existence of measure-valued solutions via vanishing viscosity limit.

Weak-strong uniqueness of solutions in the fluid-rigid body interaction.

Validation that measure-valued solutions coincide with strong solutions when they exist.

Abstract

We consider a coupled system of partial and ordinary differential equations describing the interaction between an isentropic inviscid fluid and a rigid body moving freely inside the fluid. We prove the existence of measure-valued solutions which is generated by the vanishing viscosity limit of incompressible fluid-rigid body interaction system under some physically constitutive relations. Moreover, we show that the measure-value solution coincides with strong solution on the interval of its existence. This relies on the weak-strong uniqueness analysis.