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

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, "à la Yudovich" for the Euler case, "à la Leray" for the Navier-Stokes case, as long as no collision occurs.

References in corpus (3)

• Regularity issues in the problem of fluid structure interaction
• The motion of a fluid-rigid disc system at the zero limit of the rigid disc radius
• The movement of a solid in an incompressible perfect fluid as a geodesic flow

Cited by in corpus (7)

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• On the derivation of a Stokes-Brinkman problem from Stokes equations around a random array of moving spheres
• External boundary control of the motion of a rigid body immersed in a perfect two-dimensional fluid
• Motion of a particle immersed in a two dimensional incompressible perfect fluid and point vortex dynamics
• Finite time singularity formation for moving interface Euler equations
• Measure-valued solutions and weak-strong uniqueness for the incompressible inviscid fluid-rigid body interaction