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Stability of a Steady Flow of an Incompressible Newtonian Fluid in an Exterior Domain

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Waves in Flows

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Abstract

This chapter provides a brief survey of studies on stability of a steady flow of an incompressible Newtonian fluid around a compact body \(\mathcal {B}\). Results on the long-time behavior and stability under assumptions of “sufficient smallness” of some quantities are cited and briefly described in Sect. 9.2. Results, mainly based on assumptions on spectrum of a certain associated linear operator are presented in Sect. 9.3. Finally, Sect. 9.4 contains a short note on analogous results concerning the case when body \(\mathcal {B}\) rotates.

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Acknowledgements

The research has been supported by the Grant Agency of the Czech Republic (grant No. 19-04243S) and by the Academy of Sciences of the Czech Republic (RVO 67985840).

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Authors and Affiliations

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

    Jiří Neustupa

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  1. Jiří Neustupa
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Correspondence to Jiří Neustupa .

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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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Neustupa, J. (2021). Stability of a Steady Flow of an Incompressible Newtonian Fluid in an Exterior Domain. 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_9

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