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Steady-State Navier-Stokes Flow Around a Moving Body

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Abstract

In this chapter we present an updated account of the fundamental mathematical results pertaining the steady-state flow of a Navier-Stokes liquid past a rigid body which is allowed to rotate. Precisely, we shall address questions of existence, uniqueness, regularity, asymptotic structure, generic properties, and (steady and unsteady) bifurcation. Moreover, we will perform a rather complete analysis of the longtime behavior of dynamical perturbation to the above flow, thus inferring, in particular, sufficient conditions for their stability and asymptotic stability.

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Acknowledgements

The authors acknowledge the partial support of NSF grant DMS-1614011 (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 Sciences 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 and Materials Science, University of Pittsburgh, 15261, Pittsburgh, PA, USA

    Giovanni P. Galdi

  2. Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 115 67, Praha 1, Czech Republic

    Jiří Neustupa

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  1. Giovanni P. Galdi
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  2. Jiří Neustupa
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Correspondence to Giovanni P. Galdi .

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Editors and Affiliations

  1. Graduate School of Mathematical Sciences, University of Tokyo, Meguro-ku, Tokyo, Japan

    Yoshikazu Giga

  2. Université de Toulon IMATH, Toulon, France

    Antonín Novotný

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Galdi, G.P., Neustupa, J. (2018). Steady-State Navier-Stokes Flow Around a Moving Body. In: Giga, Y., Novotný, A. (eds) Handbook of Mathematical Analysis in Mechanics of Viscous Fluids. Springer, Cham. https://doi.org/10.1007/978-3-319-13344-7_7

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