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

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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.

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Authors and Affiliations

  1. CEREMADE, UMR CNRS 7534, Université Paris-Dauphine, Place du Maréchal de Lattre de Tassigny, 75775, Paris Cedex 16, France

    Olivier Glass

  2. Institut de Mathématiques de Bordeaux, UMR CNRS 5251, Université de Bordeaux, 351 cours de la Libération, 33405, Talence Cedex, France

    Franck Sueur

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  1. Olivier Glass
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  2. Franck Sueur
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Correspondence to Franck Sueur.

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Communicated by C. Dafermos

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Glass, O., Sueur, F. Uniqueness Results for Weak Solutions of Two-Dimensional Fluid–Solid Systems. Arch Rational Mech Anal 218, 907–944 (2015). https://doi.org/10.1007/s00205-015-0876-8

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