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Lp-Theory for Incompressible Newtonian Flows

Energy Preserving Boundary Conditions, Weakly Singular Domains

  • Book
  • © 2013

Overview

Authors:
  1. Matthias Köhne

    1. Technische Universität Darmstadt, Darmstadt, Germany

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  • Publication in the field of technical sciences?

  • Includes supplementary material: sn.pub/extras

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Table of contents (8 chapters)

  1. Front Matter

    Pages 1-1
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  2. The Model

    1. Front Matter

      Pages 9-9
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    2. The Navier-Stokes Equations

      • Matthias Köhne
      Pages 11-19

    3. Energy Preserving Boundary Conditions

      • Matthias Köhne
      Pages 21-32

  3. Bounded Smooth Domains

    1. Front Matter

      Pages 33-33
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    2. L p -Theory for Incompressible Newtonian Flows

      • Matthias Köhne
      Pages 35-65

    3. Tools and Methods

      • Matthias Köhne
      Pages 67-100

    4. Maximal L p -Regularity in a Halfspace

      • Matthias Köhne
      Pages 101-114

    5. Maximal L p -Regularity in a Bent Halfspace

      • Matthias Köhne
      Pages 115-126

    6. Maximal L p -Regularity in a Bounded Smooth Domain

      • Matthias Köhne
      Pages 127-150

  4. Bounded Weakly Singular Domains

    1. Front Matter

      Pages 151-151
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    2. L p -Theory in Weakly Singular Domains

      • Matthias Köhne
      Pages 153-167

  5. Back Matter

    Pages 13-13
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Keywords

About this book

This thesis is devoted to the study of the basic equations of fluid dynamics. First Matthias Köhne focuses on the derivation of a class of boundary conditions, which is based on energy estimates, and, thus, leads to physically relevant conditions. The derived class thereby contains many prominent artificial boundary conditions, which have proved to be suitable for direct numerical simulations involving artificial boundaries. The second part is devoted to the development of a complete Lp-theory for the resulting initial boundary value problems in bounded smooth domains, i.e. the Navier-Stokes equations complemented by one of the derived energy preserving boundary conditions. Finally, the third part of this thesis focuses on the corresponding theory for bounded, non-smooth domains, where the boundary of the domain is allowed to contain a finite number of edges, provided the smooth components of the boundary that meet at such an edge are locally orthogonal.

Authors and Affiliations

  • Technische Universität Darmstadt, Darmstadt, Germany

    Matthias Köhne

About the author

Matthias Köhne earned a doctorate of Mathematics under the supervision of Prof. Dr. Dieter Bothe at the Department of Mathematics at TU Darmstadt, where his research was supported by the cluster of excellence ''Center of Smart Interfaces'' and the international research training group ''Mathematical Fluid Dynamics''.

Bibliographic Information

  • Book Title: Lp-Theory for Incompressible Newtonian Flows

  • Book Subtitle: Energy Preserving Boundary Conditions, Weakly Singular Domains

  • Authors: Matthias Köhne

  • DOI: https://doi.org/10.1007/978-3-658-01052-2

  • Publisher: Springer Spektrum Wiesbaden

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Fachmedien Wiesbaden 2013

  • Softcover ISBN: 978-3-658-01051-5Published: 06 December 2012

  • eBook ISBN: 978-3-658-01052-2Published: 06 December 2012

  • Edition Number: 1

  • Number of Pages: XI, 183

  • Number of Illustrations: 2 b/w illustrations

  • Topics: Integral Equations

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