Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

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 L^p-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

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.

• Compressible Fluids
• Fourier Analysis
• Mathematical Analysis
• Mathematical Theory
• Navier-Stokes
• Newtonian Fluids
• Viscous Fluids
• fluid- and aerodynamics

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

  Yoshikazu Giga

• Université de Toulon IMATH, Toulon, France

  Antonín Novotný

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.

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