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

  • Marco BravinEmail author


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.


Navier–Stokes equations Fluid–structure interaction Uniqueness Navier-type boundary conditions 

Mathematics Subject Classification

Primary 35Q35 Secondary 76B03 76N17 


Compliance with ethical standards

Conflict of interest

The author declares that he has no conflict of interest.


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Authors and Affiliations

  1. 1.Institut de Mathématiques de Bordeaux UMR CNRS 5251Université de BordeauxTalence CedexFrance

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