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Table of contents

  1. Front Matter
    Pages i-xxviii
    PDF

  2. Derivation of Equations for Incompressible and Compressible Fluids

    1. Front Matter
      Pages 1-1
      PDF
    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
      PDF
    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
    17. Vorticity Direction and Regularity of Solutions to the Navier-Stokes Equations
      Hugo Beirão da Veiga, Yoshikazu Giga, Zoran Grujić
      Pages 901-932
    18. Recent Advances Concerning Certain Class of Geophysical Flows
      Jinkai Li, Edriss S. Titi
      Pages 933-971
    19. Equations for Polymeric Materials
      Nader Masmoudi
      Pages 973-1005
    20. Modeling of Two-Phase Flows With and Without Phase Transitions
      Jan W. Prüss, Senjo Shimizu
      Pages 1007-1044
    21. Equations for Viscoelastic Fluids
      Xianpeng Hu, Fang-Hua Lin, Chun Liu
      Pages 1045-1073
    22. Modeling and Analysis of the Ericksen-Leslie Equations for Nematic Liquid Crystal Flows
      Matthias Hieber, Jan W. Prüss
      Pages 1075-1134
    23. Classical Well-Posedness of Free Boundary Problems in Viscous Incompressible Fluid Mechanics
      Vsevolod Alexeevich Solonnikov, Irina Vladimirovna Denisova
      Pages 1135-1220
    24. Stability of Equilibrium Shapes in Some Free Boundary Problems Involving Fluids
      Gieri Simonett, Mathias Wilke
      Pages 1221-1265
    25. Weak Solutions and Diffuse Interface Models for IncompressibleTwo-Phase Flows
      Helmut Abels, Harald Garcke
      Pages 1267-1327
    26. Water Waves with or Without Surface Tension
      Diego Córdoba, Charles Fefferman
      Pages 1329-1349

  4. Compressible Viscous Fluids

    1. Front Matter
      Pages 1351-1351
      PDF
    2. Concepts of Solutions in the Thermodynamics of Compressible Fluids
      Eduard Feireisl
      Pages 1353-1379
    3. Weak Solutions for the Compressible Navier-Stokes Equations: Existence, Stability, and Longtime Behavior
      Antonín Novotný, Hana Petzeltová
      Pages 1381-1546
    4. Weak Solutions for the Compressible Navier-Stokes Equations with Density Dependent Viscosities
      Didier Bresch, Benoît Desjardins
      Pages 1547-1599
    5. Weak Solutions to 2D and 3D Compressible Navier-Stokes Equations in Critical Cases
      P. I. Plotnikov, W. Weigant
      Pages 1601-1671
    6. Weak Solutions for the Compressible Navier-Stokes Equations in the Intermediate Regularity Class
      Misha Perepelitsa
      Pages 1673-1710
    7. Symmetric Solutions to the Viscous Gas Equations
      Song Jiang, Qiangchang Ju
      Pages 1711-1749
    8. Local and Global Solutions for the Compressible Navier-Stokes Equations Near Equilibria via the Energy Method
      Jan Burczak, Yoshihiro Shibata, Wojciech M. Zaja̧czkowski
      Pages 1751-1841
    9. Fourier Analysis Methods for the Compressible Navier-Stokes Equations
      Raphaël Danchin
      Pages 1843-1903
    10. Local and Global Existence of Strong Solutions for the Compressible Navier-Stokes Equations Near Equilibria via the Maximal Regularity
      Matthias Kotschote
      Pages 1905-1946
    11. Local and Global Solvability of Free Boundary Problems for the Compressible Navier-Stokes Equations Near Equilibria
      Irina Vladimirovna Denisova, Vsevolod Alexeevich Solonnikov
      Pages 1947-2035
    12. Global Existence of Regular Solutions with Large Oscillations and Vacuum for Compressible Flows
      Jing Li, Zhou Ping Xin
      Pages 2037-2083
    13. Global Existence of Classical Solutions and Optimal Decay Rate for Compressible Flows via the Theory of Semigroups
      Yoshihiro Shibata, Yuko Enomoto
      Pages 2085-2181
    14. Finite Time Blow-Up of Regular Solutions for Compressible Flows
      Xiangdi Huang, Zhou Ping Xin
      Pages 2183-2261
    15. Blow-Up Criteria of Strong Solutions and Conditional Regularity of Weak Solutions for the Compressible Navier-Stokes Equations
      Yongzhong Sun, Zhifei Zhang
      Pages 2263-2324
    16. Well-Posedness and Asymptotic Behavior for Compressible Flows in One Dimension
      Yuming Qin
      Pages 2325-2420
    17. Well-Posedness of the IBVPs for the 1D Viscous Gas Equations
      Alexander Zlotnik
      Pages 2421-2493
    18. Waves in Compressible Fluids: Viscous Shock, Rarefaction, and Contact Waves
      Akitaka Matsumura
      Pages 2495-2548
    19. Existence of Stationary Weak Solutions for Isentropic and Isothermal Compressible Flows
      Song Jiang, Chunhui Zhou
      Pages 2549-2594
    20. Existence of Stationary Weak Solutions for Compressible Heat Conducting Flows
      PiotrBogusł aw Mucha, Milan Pokorný, Ewelina Zatorska
      Pages 2595-2662

About this book

Introduction

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.

Keywords

Compressible Fluids Fourier Analysis Mathematical Analysis Mathematical Theory Navier-Stokes Newtonian Fluids Viscous Fluids

Editors and affiliations

  • Yoshikazu Giga
    • 1
  • Antonín Novotný
    • 2
  1. 1.Graduate School of Mathematical SciencesUniversity of TokyoMeguro-kuJapan
  2. 2.Université de Toulon IMATHToulonFrance

Bibliographic information