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Time-Periodic Solutions to the Navier-Stokes Equations

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Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

Abstract

The Navier-Stokes equations with time-periodic data are investigated with respect to solutions of the same period. In the physical terms, such a system models the flow of a viscous liquid under the influence of a time-periodic force. The three most relevant types of flow domains, from a physical point of view, are considered: a bounded domain, an exterior domain, and an infinite pipe. Methods to show existence of both weak and strong solutions are introduced. Moreover, questions regarding regularity, uniqueness, and asymptotic structure at spatial infinity of solutions are addressed.

The work of G.P. Galdi was partially supported by the NSF grant DMS-1614011

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Author information

Authors and Affiliations

  1. Department of Mechanical Engineering and Materials Science, University of Pittsburgh, 15261, Pittsburgh, PA, USA

    Giovanni P. Galdi

  2. Fachbereich Mathematik, Technische Universität Darmstadt, Room: S2—15 /408, Schlossgartenstr. 7, 64289, Darmstadt, Germany

    Mads Kyed

Authors
  1. Giovanni P. Galdi
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  2. Mads Kyed
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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., Kyed, M. (2018). Time-Periodic Solutions to the Navier-Stokes Equations. 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_10

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