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Stability of Steady Flow Past a Rotating Body

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Mathematical Fluid Dynamics, Present and Future

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 183))

Abstract

We study stability of a steady solution of the mathematical model describing the flow of a viscous incompressible fluid past a rotating body. We derive a sufficient condition for stability, which requires the \(L^1\)– and \(L^2\)–integrability on the time interval \((0,\infty )\) of the semigroup generated by the relevant linear operator, applied to a finite family of suitable functions, in a norm restricted to a “sufficiently large” bounded region around the body. No assumption on the smallness of the steady solution is required.

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Acknowledgements

The authors thank the partial support of NSF grant DMS-1311983 (G.P. Galdi), and the Grant Agency of the Czech Republic, grant No. 13-00522S, and Academy of Sciences of the Czech Republic, RVO 67985840 (J. Neustupa). This work was also partially supported by the Department of Mechanical Engineering and Materials Science of the University of Pittsburgh, that hosted the visit of J. Neustupa in Spring 2015.

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Pittsburgh, Pittsburgh, USA

    Giovanni Paolo Galdi

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

    Jiří Neustupa

Authors
  1. Giovanni Paolo Galdi
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  2. Jiří Neustupa
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Correspondence to Giovanni Paolo Galdi .

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Editors and Affiliations

  1. Department of Mathematics, Waseda University, Tokyo, Japan

    Yoshihiro Shibata

  2. Department of Mathematics, Waseda University, Tokyo, Japan

    Yukihito Suzuki

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Galdi, G.P., Neustupa, J. (2016). Stability of Steady Flow Past a Rotating Body. In: Shibata, Y., Suzuki, Y. (eds) Mathematical Fluid Dynamics, Present and Future. Springer Proceedings in Mathematics & Statistics, vol 183. Springer, Tokyo. https://doi.org/10.1007/978-4-431-56457-7_4

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