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Topics in the Mathematical Theory of Interactions of Incompressible Viscous Fluid with Rigid Bodies

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Fluid-Structure Interaction and Biomedical Applications

Part of the book series: Advances in Mathematical Fluid Mechanics ((AMFM))

Abstract

In this paper, we review recent results devoted to the interactions between a collection of rigid bodies \((\mathcal{B}_{i})_{i=1,\ldots,n}\) and a surrounding viscous fluid \(\mathcal{L}\), the whole system filling a container \(\Omega \). We assume that the motion of \(\mathcal{L}\) (resp. the rigid bodies \(\mathcal{B}_{i}\)) is governed by the incompressible Navier Stokes equations (resp. Newton laws), and that velocities and stress tensors are continuous at the fluid/body interfaces. Our concern is the well-posedness of the associated Cauchy problem, with a specific eye towards the handling of contact between bodies or between one body and the container boundary.

MSC2010: 35Q35, 35B44, 35Q74, 74F10, 76D03, 76D05

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Authors and Affiliations

  1. Université Paris Dauphine, Paris, France

    Matthieu Hillairet

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  1. Matthieu Hillairet
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Correspondence to Matthieu Hillairet .

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  1. Department of Technical Mathematics, Czech Technical University in Prague, Prague, Czech Republic

    Tomáš Bodnár

  2. Swanson School of Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania, USA

    Giovanni P. Galdi

  3. Institute of Mathematics, Academy of Sciences of the Czech Republic, Prague 1, Czech Republic

    Šárka Nečasová

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Hillairet, M. (2014). Topics in the Mathematical Theory of Interactions of Incompressible Viscous Fluid with Rigid Bodies. In: Bodnár, T., Galdi, G., Nečasová, Š. (eds) Fluid-Structure Interaction and Biomedical Applications. Advances in Mathematical Fluid Mechanics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0822-4_4

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