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Recent Developments of Mathematical Fluid Mechanics

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  • © 2016

Overview

Editors:
  1. Herbert Amann

    1. Universität of Zürich, Institut für Mathematik, Zürich, Switzerland

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  2. Yoshikazu Giga

    1. University of Tokyo, Graduate School of Mathematical Sciences, Tokyo, Japan

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  3. Hideo Kozono

    1. Department of Mathematics, Waseda University, Tokyo, Japan

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  4. Hisashi Okamoto

    1. Research Institute for Mathematical Sciences, Kyoto University Kitashirakawa, Kyoto, Japan

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  5. Masao Yamazaki

    1. Department of Mathematics, Waseda University, Tokyo, Japan

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  • Presents interesting results and open questions closely related to
  • the Millennium Seven Problems proposed by the Clay Mathematical Institute
  • Authors are experts of the Navier-Stokes and the Euler equations
  • Valuable read especially also for graduate students and young researchers

Part of the book series: Advances in Mathematical Fluid Mechanics (AMFM)

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Table of contents (24 chapters)

  1. Front Matter

    Pages i-ix
    Download chapter PDF

  2. The Work of Yoshihiro Shibata

    • Herbert Amann, Yoshikazu Giga, Hisashi Okamoto, Hideo Kozono, Masaso Yamazaki
    Pages 1-12

  3. Existence of Weak Solutions for a Diffuse Interface Model of Power-Law Type Two-Phase Flows

    • Helmut Abels, Lars Diening, Yutaka Terasawa
    Pages 13-23

  4. Stationary Solutions for a Navier-Stokes/Cahn-Hilliard System with Singular Free Energies

    • Helmut Abels, Josef Weber
    Pages 25-41

  5. Parabolic Equations on Uniformly Regular Riemannian Manifolds and Degenerate Initial Boundary Value Problems

    • Herbert Amann
    Pages 43-77

  6. A Generalization of Some Regularity Criteria to the Navier–Stokes Equations Involving One Velocity Component

    • Šimon Axmann, Milan Pokorný
    Pages 79-97

  7. On the Singular p-Laplacian System Under Navier Slip Type Boundary Conditions: The Gradient-Symmetric Case

    • H. Beirão da Veiga
    Pages 99-109

  8. Thermodynamically Consistent Modeling for Dissolution/Growth of Bubbles in an Incompressible Solvent

    • Dieter Bothe, Kohei Soga
    Pages 111-134

  9. On Unsteady Internal Flows of Bingham Fluids Subject to Threshold Slip on the Impermeable Boundary

    • Miroslav Bulíček, Josef Málek
    Pages 135-156

  10. Inhomogeneous Boundary Value Problems in Spaces of Higher Regularity

    • Robert Denk, Tim Seger
    Pages 157-173

  11. Blow-Up Criterion for 3D Navier-Stokes Equations and Landau-Lifshitz System in a Bounded Domain

    • Jishan Fan, Tohru Ozawa
    Pages 175-182

  12. Local Regularity Results for the Instationary Navier-Stokes Equations Based on Besov Space Type Criteria

    • Reinhard Farwig
    Pages 183-214

  13. On Global Well/Ill-Posedness of the Euler-Poisson System

    • Eduard Feireisl
    Pages 215-231

  14. On the Motion of a Liquid-Filled Rigid Body Subject to a Time-Periodic Torque

    • Giovanni P. Galdi, Giusy Mazzone, Mahdi Mohebbi
    Pages 233-255

  15. Seeking a Proof of Xie’s Inequality: On the Conjecture That \(\mu _{m} \rightarrow \infty \)

    • John G. Heywood
    Pages 257-273

  16. Bounded Analyticity of the Stokes Semigroup on Spaces of Bounded Functions

    • Matthias Hieber, Paolo Maremonti
    Pages 275-289

  17. On the Weak Solution of the Fluid-Structure Interaction Problem for Shear-Dependent Fluids

    • Anna Hundertmark, Mária Lukáčová-Medviďová, Šárka Nečasová
    Pages 291-319

  18. Stability of Time Periodic Solutions for the Rotating Navier-Stokes Equations

    • Tsukasa Iwabuchi, Alex Mahalov, Ryo Takada
    Pages 321-335

  19. Weighted L p − L q Estimates of Stokes Semigroup in Half-Space and Its Application to the Navier-Stokes Equations

    • Takayuki Kobayashi, Takayuki Kubo
    Pages 337-349

  20. On Vorticity Formulation for Viscous Incompressible Flows in R + 3

    • Humiya Kosaka, Yasunori Maekawa
    Pages 351-374
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Keywords

About this book

The aim of this proceeding is addressed to present recent developments of the mathematical research on the Navier-Stokes equations, the Euler equations and other related equations.  In particular, we are interested in such problems as:
1) existence, uniqueness and regularity of weak solutions2) stability and its asymptotic behavior of the rest motion and the steady state3) singularity and blow-up of weak and strong solutions4) vorticity and energy conservation5) fluid motions around the rotating axis or outside of the rotating body6) free boundary problems7) maximal regularity theorem and other abstract theorems for mathematical fluid mechanics.

Editors and Affiliations

  • Universität of Zürich, Institut für Mathematik, Zürich, Switzerland

    Herbert Amann

  • University of Tokyo, Graduate School of Mathematical Sciences, Tokyo, Japan

    Yoshikazu Giga

  • Department of Mathematics, Waseda University, Tokyo, Japan

    Hideo Kozono, Masao Yamazaki

  • Research Institute for Mathematical Sciences, Kyoto University Kitashirakawa, Kyoto, Japan

    Hisashi Okamoto

Bibliographic Information

  • Book Title: Recent Developments of Mathematical Fluid Mechanics

  • Editors: Herbert Amann, Yoshikazu Giga, Hideo Kozono, Hisashi Okamoto, Masao Yamazaki

  • Series Title: Advances in Mathematical Fluid Mechanics

  • DOI: https://doi.org/10.1007/978-3-0348-0939-9

  • Publisher: Birkhäuser Basel

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer Basel 2016

  • Hardcover ISBN: 978-3-0348-0938-2Published: 29 March 2016

  • eBook ISBN: 978-3-0348-0939-9Published: 17 March 2016

  • Series ISSN: 2297-0320

  • Series E-ISSN: 2297-0339

  • Edition Number: 1

  • Number of Pages: IX, 482

  • Number of Illustrations: 3 b/w illustrations, 1 illustrations in colour

  • Topics: Partial Differential Equations

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