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Energy Equality and Uniqueness of Weak Solutions of a “Viscous Incompressible Fluid + Rigid Body” System with Navier Slip-with-Friction Conditions in a 2D Bounded Domain

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Abstract

The existence of weak solutions to the “viscous incompressible fluid + rigid body” system with Navier slip-with-friction conditions in a 3D bounded domain has been recently proved by Gérard-Varet and Hillairet (Commun Pure Appl Math 67(12):2022–2076, 2014). In 2D for a fluid alone (without any rigid body) it is well-known since Leray that weak solutions are unique, continuous in time with \( L^{2} \) regularity in space and satisfy the energy equality. In this paper we prove that these properties also hold for the 2D “viscous incompressible fluid + rigid body” system with Navier slip-with-friction conditions.

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

    Marco Bravin

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  1. Marco Bravin
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Correspondence to Marco Bravin.

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Communicated by G. P. Galdi

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The author was supported by the Agence Nationale de la Recherche, Project IFSMACS, Grant ANR-15-CE40-0010 and the Conseil Régional d’Aquitaine, Grant 2015.1047.CP.

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Bravin, M. Energy Equality and Uniqueness of Weak Solutions of a “Viscous Incompressible Fluid + Rigid Body” System with Navier Slip-with-Friction Conditions in a 2D Bounded Domain. J. Math. Fluid Mech. 21, 23 (2019). https://doi.org/10.1007/s00021-019-0425-6

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  • DOI: https://doi.org/10.1007/s00021-019-0425-6

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