Weak-Strong Uniqueness for a Rigid Body Immersed in an Inviscid Compressible Fluid

TL;DR

This paper proves the local-in-time existence and weak-strong uniqueness of solutions for a model of a rigid body immersed in an inviscid compressible fluid, using a vanishing viscosity limit approach.

Contribution

It introduces the first mathematical proof of weak-strong uniqueness for compressible inviscid fluid-structure interaction models.

Findings

Established local-in-time existence of dissipative measure-valued solutions.

Proved weak-strong uniqueness property for these solutions.

Developed a novel approximation technique for test functions depending on viscosity.

Abstract

We consider the coupled motion of a free rigid body immersed in an inviscid compressible isentropic fluid. By means of a vanishing viscosity limit, we obtain the local-in-time existence of a dissipative measure-valued solution to the model. Moreover, we establish the weak-strong uniqueness property of the obtained measure-valued solution. To our knowledge, this is the first mathematical result on compressible inviscid fluid-structure interaction. The key novel technique is the construction of a suitable approximation of the test function in the weak formulation of the inviscid system, as the space of test functions depends on the viscosity parameter.