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A Special Class of Weak Solutions of the Navier-Stokes Equations in Arbitrary Three-dimensional Domains

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Topics in Nonlinear Analysis

Part of the book series: Progress in Nonlinear Differential Equations and Their Applications ((PNLDE,volume 35))

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Abstract

Let Ω ⊆ ℝ3 be any domain, i.e. any nonempty open connected set in ℝ3. Here we are mainly interested in unbounded domains, δΩ denotes the boundary of Ω. In Ω we consider the system of the Navier-Stokes equations of the form describing the unknown velocity field u = (u 1,u 2,u 3) and the unknown pressure p of a flow within [0, T) x Ω where 0 < T < ∞; f = (f 1, f 2, f 3) denotes the given force and u 0 the given initial velocity at t = 0.

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Author information

Authors and Affiliations

  1. Fachbereich Mathematik/Informatik, Universität Paderborn, D-33095, Paderborn, Germany

    Hermann Sohr

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  1. Hermann Sohr
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Editors and Affiliations

  1. Mathematik Universität GH Kassel, Heinrich-Plett-Strasse 40, D-34132, Kassel, Germany

    Joachim Escher

  2. Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, TN, 37240, USA

    Gieri Simonett

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© 1999 Springer Basel AG

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Sohr, H. (1999). A Special Class of Weak Solutions of the Navier-Stokes Equations in Arbitrary Three-dimensional Domains. In: Escher, J., Simonett, G. (eds) Topics in Nonlinear Analysis. Progress in Nonlinear Differential Equations and Their Applications, vol 35. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8765-6_27

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  • DOI: https://doi.org/10.1007/978-3-0348-8765-6_27

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9764-8

  • Online ISBN: 978-3-0348-8765-6

  • eBook Packages: Springer Book Archive

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