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Waves in Flows pp 203–237Cite as

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A Review on Rigorous Derivation of Reduced Models for Fluid–Structure Interaction Systems

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Abstract

In this paper we review and systematize the mathematical theory on justification of sixth-order thin-film equations as reduced models for various fluid–structure interaction systems in which fluids are lubricating underneath elastic structures. Justification is based on careful examination of energy estimates, weak convergence results of solutions of the original fluid–structure interaction systems to the solution of the sixth-order thin-film equation, and quantitative error estimates that provide even strong convergence results.

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Author information

Authors and Affiliations

  1. Faculty of Electrical Engineering and Computing, University of Zagreb, Zagreb, Croatia

    Mario Bukal

  2. Faculty of Science, Department of Mathematics, University of Zagreb, , Zagreb, Croatia

    Boris Muha

Authors
  1. Mario Bukal
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  2. Boris Muha
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Correspondence to Boris Muha .

Editor information

Editors and Affiliations

  1. Department of Technical Mathematics, Faculty of Mechanical Engineering, Czech Technical University, Prague, Czech Republic

    Tomáš Bodnár

  2. Department of Mechanical Engineering, University of Pittsburgh, Pittsburgh, PA, USA

    Giovanni P. Galdi

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

    Šárka Nečasová

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Bukal, M., Muha, B. (2021). A Review on Rigorous Derivation of Reduced Models for Fluid–Structure Interaction Systems. In: Bodnár, T., Galdi, G.P., Nečasová, Š. (eds) Waves in Flows. Advances in Mathematical Fluid Mechanics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-68144-9_8

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