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The Nonstationary Stokes and Navier-Stokes Flows Through an Aperture

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Contributions to Current Challenges in Mathematical Fluid Mechanics

Part of the book series: Advances in Mathematical Fluid Mechanics ((AMFM))

Abstract

We consider the nonstationary Stokes and Navier—Stokes flows in aperture domains Ω ⊂ R n, n ≥ 3. We develop the L q -L r estimates of the Stokes semigroup and apply them to the Navier—Stokes initial value problem. As a result, we obtain the global existence of a unique strong solution, which satisfies the vanishing flux condition through the aperture and some sharp decay properties as t→∞, when the initial velocity is sufficiently small in the L n space. Such a global existence theorem is up to now well known in the cases of the whole and half spaces, bounded and exterior domains.

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Authors and Affiliations

  1. Fachbereich Mathematik, Technische Universität Darmstadt, Darmstadt, D-64289, Germany

    Toshiaki Hishida

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  1. Toshiaki Hishida
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Editors and Affiliations

  1. School of Engineering Department of Mechanical Engineering, University of Pittsburgh, 3700 O’Hara Street, Pittsburgh, PA, 15261, USA

    Giovanni P. Galdi

  2. Department of Mathematics, University of British Columbia, Vancouver, BC, Canada, V6T 1Y4

    John G. Heywood

  3. Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 293/294, 69120, Heidelberg, Germany

    Rolf Rannacher

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Hishida, T. (2004). The Nonstationary Stokes and Navier-Stokes Flows Through an Aperture. In: Galdi, G.P., Heywood, J.G., Rannacher, R. (eds) Contributions to Current Challenges in Mathematical Fluid Mechanics. Advances in Mathematical Fluid Mechanics. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7877-7_4

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  • DOI: https://doi.org/10.1007/978-3-0348-7877-7_4

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9606-1

  • Online ISBN: 978-3-0348-7877-7

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