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Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

  • Reference work
  • © 2018

Overview

Editors:
  1. Yoshikazu Giga

    1. Graduate School of Mathematical Sciences, University of Tokyo, Meguro-ku, Japan

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    You can also search for this editor in PubMed   Google Scholar

  2. Antonín Novotný

    1. Université de Toulon IMATH, Toulon, France

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

  • Includes equations describing special solutions
  • Contains sections on both incompressible fluids and compressible fluids
  • Renowned international researchers serve as editors
  • Includes supplementary material: sn.pub/extras

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Table of contents (53 entries)

  1. Front Matter

    Pages i-xxviii
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  2. Derivation of Equations for Incompressible and Compressible Fluids

    1. Front Matter

      Pages 1-1
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    2. Derivation of Equations for Continuum Mechanics and Thermodynamics of Fluids

      • Josef Málek, Vít Průša
      Pages 3-72

    3. Variational Modeling and Complex Fluids

      • Mi-Ho Giga, Arkadz Kirshtein, Chun Liu
      Pages 73-113

  3. Incompressible Fluids

    1. Front Matter

      Pages 115-115
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    2. The Stokes Equation in the Lp-Setting: Well-Posedness and Regularity Properties

      • Matthias Hieber, Jürgen Saal
      Pages 117-206

    3. Stokes Problems in Irregular Domains with Various Boundary Conditions

      • Sylvie Monniaux, Zhongwei Shen
      Pages 207-248

    4. Leray’s Problem on Existence of Steady-State Solutions for the Navier-Stokes Flow

      • Mikhail V. Korobkov, Konstantin Pileckas, Remigio Russo
      Pages 249-297

    5. Stationary Navier-Stokes Flow in Exterior Domains and Landau Solutions

      • Toshiaki Hishida
      Pages 299-339

    6. Steady-State Navier-Stokes Flow Around a Moving Body

      • Giovanni P. Galdi, Jiří Neustupa
      Pages 341-417

    7. Stokes Semigroups, Strong, Weak, and Very Weak Solutions for General Domains

      • Reinhard Farwig, Hideo Kozono, Hermann Sohr
      Pages 419-459

    8. Self-Similar Solutions to the Nonstationary Navier-Stokes Equations

      • Hao Jia, Vladimir Šverák, Tai-Peng Tsai
      Pages 461-507

    9. Time-Periodic Solutions to the Navier-Stokes Equations

      • Giovanni P. Galdi, Mads Kyed
      Pages 509-578

    10. Large Time Behavior of the Navier-Stokes Flow

      • Lorenzo Brandolese, Maria E. Schonbek
      Pages 579-645

    11. Critical Function Spaces for the Well-Posedness of the Navier-Stokes Initial Value Problem

      • Isabelle Gallagher
      Pages 647-685

    12. Existence and Stability of Viscous Vortices

      • Thierry Gallay, Yasunori Maekawa
      Pages 687-727

    13. Models and Special Solutions of the Navier-Stokes Equations

      • Hisashi Okamoto
      Pages 729-780

    14. The Inviscid Limit and Boundary Layers for Navier-Stokes Flows

      • Yasunori Maekawa, Anna Mazzucato
      Pages 781-828

    15. Regularity Criteria for Navier-Stokes Solutions

      • Gregory Seregin, Vladimir Šverák
      Pages 829-867

    16. Stable Self-Similar Profiles for Two 1D Models of the 3D Axisymmetric Euler Equations

      • Thomas Yizhao Hou, Pengfei Liu
      Pages 869-899
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Keywords

About this book

Mathematics has always played a key role for researches in fluid mechanics. The purpose of this handbook is to give an overview of items that are key to handling problems in fluid mechanics. Since the field of fluid mechanics is huge, it is almost impossible to cover many topics. In this handbook, we focus on mathematical analysis on viscous Newtonian fluid. The first part is devoted to mathematical analysis on incompressible fluids while part 2 is devoted to compressible fluids.

Editors and Affiliations

  • Graduate School of Mathematical Sciences, University of Tokyo, Meguro-ku, Japan

    Yoshikazu Giga

  • Université de Toulon IMATH, Toulon, France

    Antonín Novotný

About the editors

Yoshikazu Giga is Professor at the Graduate School of Mathematical Sciences of the University of Tokyo, Japan. He is a fellow of the American Mathematical Society as well as of the Japan Society for Industrial and Applied Mathematics. Through his more than two hundred papers and two monographs, he has substantially contributed to the theory of parabolic partial differential equations including geometric evolution equations, semilinear heat equations as well as the incompressible Navier-Stokes equations. He has received several prizes including the Medal of Honour with Purple Ribbon from the government of Japan.

Antonin Novotny is Professor at the Department of Mathematics of the University of Toulon and member of the Institute of Mathematics of the University of Toulon, France. Co-author of more than hundred papers and two monographs, he is one of the leading experts in the theory of compressible Navier-Stokes equations.

Bibliographic Information

  • Book Title: Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

  • Editors: Yoshikazu Giga, Antonín Novotný

  • DOI: https://doi.org/10.1007/978-3-319-13344-7

  • Publisher: Springer Cham

  • eBook Packages: Mathematics and Statistics, Reference Module Computer Science and Engineering

  • Copyright Information: Springer International Publishing AG, part of Springer Nature 2018

  • Hardcover ISBN: 978-3-319-13343-0Published: 07 May 2018

  • eBook ISBN: 978-3-319-13344-7Published: 19 April 2018

  • Edition Number: 1

  • Number of Pages: XXVIII, 3045

  • Number of Illustrations: 34 b/w illustrations, 28 illustrations in colour

  • Topics: Analysis, Mathematical Physics, Fluid- and Aerodynamics

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