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Lp-Theory for Incompressible Newtonian Flows

Energy Preserving Boundary Conditions, Weakly Singular Domains

  • Matthias Köhne

Table of contents

  1. Front Matter
    Pages 1-1
  2. The Model

    1. Front Matter
      Pages 9-9
    2. Matthias Köhne
      Pages 11-19
    3. Matthias Köhne
      Pages 21-32
  3. Bounded Smooth Domains

    1. Front Matter
      Pages 33-33
    2. Matthias Köhne
      Pages 35-65
    3. Matthias Köhne
      Pages 67-100
    4. Matthias Köhne
      Pages 101-114
    5. Matthias Köhne
      Pages 115-126
    6. Matthias Köhne
      Pages 127-150
  4. Bounded Weakly Singular Domains

    1. Front Matter
      Pages 151-151
    2. Matthias Köhne
      Pages 153-167
  5. Back Matter
    Pages 13-13

About this book

Introduction

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.

Contents

·         Navier-Stokes Equations

·         Energy Preserving Boundary Condition

·         Weakly Singular Domain

·         Maximal Lp-Regularity

Target Groups

·         Scientists, lecturers and graduate students in the fields of mathematical fluid dynamics and partial differential equations as well as experts in applied analysis.

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''.

Keywords

Energy Preserving Boundary Condition Mathematical Fluid Dynamics Maximal Lp-Regularity Navier-Stokes Equations Weakly Singular Domain

Authors and affiliations

  • Matthias Köhne
    • 1
  1. 1.Technische Universität DarmstadtDarmstadtGermany

Bibliographic information

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