Archive for Rational Mechanics and Analysis

, Volume 218, Issue 2, pp 907–944 | Cite as

Uniqueness Results for Weak Solutions of Two-Dimensional Fluid–Solid Systems

  • Olivier Glass
  • Franck Sueur


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.


Weak Solution Rigid Body Euler Equation Strong Solution Uniqueness Result 
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© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.CEREMADE, UMR CNRS 7534, Université Paris-DauphineParis Cedex 16France
  2. 2.Institut de Mathématiques de Bordeaux, UMR CNRS 5251Université de BordeauxTalence CedexFrance

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