Handbook of Mathematical Analysis in Mechanics of Viscous Fluids

Edited by Yoshikazu Giga () and Antonín Novotný ()

in Springer Books from Springer

Date: 2018
ISBN: 978-3-319-13344-7
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Chapters in this book:

Ch 1 Derivation of Equations for Continuum Mechanics and Thermodynamics of Fluids

Josef Málek and Vít Průša

Ch 2 Variational Modeling and Complex Fluids

Mi-Ho Giga, Arkadz Kirshtein and Chun Liu

Ch 3 The Stokes Equation in the L p -Setting: Well-Posedness and Regularity Properties

Matthias Hieber and Jürgen Saal

Ch 4 Stokes Problems in Irregular Domains with Various Boundary Conditions

Sylvie Monniaux and Zhongwei Shen

Ch 5 Leray’s Problem on Existence of Steady-State Solutions for the Navier-Stokes Flow

Mikhail V. Korobkov, Konstantin Pileckas and Remigio Russo

Ch 6 Stationary Navier-Stokes Flow in Exterior Domains and Landau Solutions

Toshiaki Hishida

Ch 7 Steady-State Navier-Stokes Flow Around a Moving Body

Giovanni P. Galdi and Jiří Neustupa

Ch 8 Stokes Semigroups, Strong, Weak, and Very Weak Solutions for General Domains

Reinhard Farwig, Hideo Kozono and Hermann Sohr

Ch 9 Self-Similar Solutions to the Nonstationary Navier-Stokes Equations

Hao Jia, Vladimir Šverák and Tai-Peng Tsai

Ch 10 Time-Periodic Solutions to the Navier-Stokes Equations

Giovanni P. Galdi and Mads Kyed

Ch 11 Large Time Behavior of the Navier-Stokes Flow

Lorenzo Brandolese and Maria E. Schonbek

Ch 12 Critical Function Spaces for the Well-Posedness of the Navier-Stokes Initial Value Problem

Isabelle Gallagher

Ch 13 Existence and Stability of Viscous Vortices

Thierry Gallay and Yasunori Maekawa

Ch 14 Models and Special Solutions of the Navier-Stokes Equations

Hisashi Okamoto

Ch 15 The Inviscid Limit and Boundary Layers for Navier-Stokes Flows

Yasunori Maekawa and Anna Mazzucato

Ch 16 Regularity Criteria for Navier-Stokes Solutions

Gregory Seregin and Vladimir Šverák

Ch 17 Stable Self-Similar Profiles for Two 1D Models of the 3D Axisymmetric Euler Equations

Thomas Yizhao Hou and Pengfei Liu

Ch 18 Vorticity Direction and Regularity of Solutions to the Navier-Stokes Equations

Hugo Beirão da Veiga, Yoshikazu Giga and Zoran Grujić

Ch 19 Recent Advances Concerning Certain Class of Geophysical Flows

Jinkai Li and Edriss S. Titi

Ch 20 Equations for Polymeric Materials

Nader Masmoudi

Ch 21 Modeling of Two-Phase Flows With and Without Phase Transitions

Jan W. Prüss and Senjo Shimizu

Ch 22 Equations for Viscoelastic Fluids

Xianpeng Hu, Fang-Hua Lin and Chun Liu

Ch 23 Modeling and Analysis of the Ericksen-Leslie Equations for Nematic Liquid Crystal Flows

Matthias Hieber and Jan W. Prüss

Ch 24 Classical Well-Posedness of Free Boundary Problems in Viscous Incompressible Fluid Mechanics

Vsevolod Alexeevich Solonnikov and Irina Vladimirovna Denisova

Ch 25 Stability of Equilibrium Shapes in Some Free Boundary Problems Involving Fluids

Gieri Simonett and Mathias Wilke

Ch 26 Weak Solutions and Diffuse Interface Models for IncompressibleTwo-Phase Flows

Helmut Abels and Harald Garcke

Ch 27 Water Waves with or Without Surface Tension

Diego Córdoba and Charles Fefferman

Ch 28 Concepts of Solutions in the Thermodynamics of Compressible Fluids

Eduard Feireisl

Ch 29 Weak Solutions for the Compressible Navier-Stokes Equations: Existence, Stability, and Longtime Behavior

Antonín Novotný and Hana Petzeltová

Ch 30 Weak Solutions for the Compressible Navier-Stokes Equations with Density Dependent Viscosities

Didier Bresch and Benoît Desjardins

Ch 31 Weak Solutions to 2D and 3D Compressible Navier-Stokes Equations in Critical Cases

P. I. Plotnikov and W. Weigant

Ch 32 Weak Solutions for the Compressible Navier-Stokes Equations in the Intermediate Regularity Class

Misha Perepelitsa

Ch 33 Symmetric Solutions to the Viscous Gas Equations

Song Jiang and Qiangchang Ju

Ch 34 Local and Global Solutions for the Compressible Navier-Stokes Equations Near Equilibria via the Energy Method

Jan Burczak, Yoshihiro Shibata and Wojciech M. Zaja̧czkowski

Ch 35 Fourier Analysis Methods for the Compressible Navier-Stokes Equations

Raphaël Danchin

Ch 36 Local and Global Existence of Strong Solutions for the Compressible Navier-Stokes Equations Near Equilibria via the Maximal Regularity

Matthias Kotschote

Ch 37 Local and Global Solvability of Free Boundary Problems for the Compressible Navier-Stokes Equations Near Equilibria

Irina Vladimirovna Denisova and Vsevolod Alexeevich Solonnikov

Ch 38 Global Existence of Regular Solutions with Large Oscillations and Vacuum for Compressible Flows

Jing Li and Zhou Ping Xin

Ch 39 Global Existence of Classical Solutions and Optimal Decay Rate for Compressible Flows via the Theory of Semigroups

Yoshihiro Shibata and Yuko Enomoto

Ch 40 Finite Time Blow-Up of Regular Solutions for Compressible Flows

Xiangdi Huang and Zhou Ping Xin

Ch 41 Blow-Up Criteria of Strong Solutions and Conditional Regularity of Weak Solutions for the Compressible Navier-Stokes Equations

Yongzhong Sun and Zhifei Zhang

Ch 42 Well-Posedness and Asymptotic Behavior for Compressible Flows in One Dimension

Yuming Qin

Ch 43 Well-Posedness of the IBVPs for the 1D Viscous Gas Equations

Alexander Zlotnik

Ch 44 Waves in Compressible Fluids: Viscous Shock, Rarefaction, and Contact Waves

Akitaka Matsumura

Ch 45 Existence of Stationary Weak Solutions for Isentropic and Isothermal Compressible Flows

Song Jiang and Chunhui Zhou

Ch 46 Existence of Stationary Weak Solutions for Compressible Heat Conducting Flows

PiotrBogusł aw Mucha, Milan Pokorný and Ewelina Zatorska

Ch 47 Existence and Uniqueness of Strong Stationary Solutions for Compressible Flows

Ondřej Kreml, Piotr Bogusł aw Mucha and Milan Pokorný

Ch 48 Low Mach Number Limits and Acoustic Waves

Ning Jiang and Nader Masmoudi

Ch 49 Singular Limits for Models of Compressible, Viscous, Heat Conducting, and/or Rotating Fluids

Eduard Feireisl

Ch 50 Scale Analysis of Compressible Flows from an Application Perspective

Rupert Klein

Ch 51 Weak and Strong Solutions of Equations of Compressible Magnetohydrodynamics

Xavier Blanc and Bernard Ducomet

Ch 52 Multi-Fluid Models Including Compressible Fluids

Didier Bresch, Benoît Desjardins, Jean-Michel Ghidaglia, Emmanuel Grenier and Matthieu Hillairet

Ch 53 Solutions for Models of Chemically Reacting Compressible Mixtures

Vincent Giovangigli

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DOI: 10.1007/978-3-319-13344-7

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