Uniqueness results for weak solutions of two-dimensional fluid-solid systems

TL;DR

This paper investigates the uniqueness of weak solutions for two-dimensional fluid-solid systems, specifically for inviscid and viscous fluids, under conditions avoiding collision, extending classical results to these coupled systems.

Contribution

It provides new uniqueness results for weak solutions of fluid-solid systems in 2D, covering both Euler and Navier-Stokes models, under collision-free assumptions.

Findings

Uniqueness of weak solutions for Euler-based fluid-solid systems.

Uniqueness of weak solutions for Navier-Stokes-based fluid-solid systems.

Results extend classical fluid dynamics theories to coupled fluid-solid interactions.

Abstract

In this paper, we consider two systems modelling the evolution of a rigid body in an incompressible fluid in a bounded domain of the plane. The first system corresponds to an inviscid fluid driven by the Euler equation whereas the other one corresponds to a viscous fluid driven by the Navier-Stokes system. In both cases we investigate the uniqueness of weak solutions, "\`a la Yudovich" for the Euler case, "\`a la Leray" for the Navier-Stokes case, as long as no collision occurs.