© 2016

Recent Developments of Mathematical Fluid Mechanics

  • Herbert Amann
  • Yoshikazu Giga
  • Hideo Kozono
  • Hisashi Okamoto
  • Masao Yamazaki


  • 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 Advances in Mathematical Fluid Mechanics book series (AMFM)

Table of contents

  1. Front Matter
    Pages i-ix
  2. Herbert Amann, Yoshikazu Giga, Hisashi Okamoto, Hideo Kozono, Masaso Yamazaki
    Pages 1-12
  3. Giovanni P. Galdi, Giusy Mazzone, Mahdi Mohebbi
    Pages 233-255
  4. Anna Hundertmark, Mária Lukáčová-Medviďová, Šárka Nečasová
    Pages 291-319
  5. Tsukasa Iwabuchi, Alex Mahalov, Ryo Takada
    Pages 321-335
  6. Humiya Kosaka, Yasunori Maekawa
    Pages 351-374

About this book


The book addresses recent developments of the mathematical research on the Navier-Stokes and Euler equations

as well as on related problems. In particular, there are covered:


1) existence, uniqueness, and the regularity of weak solutions;

2) stability of the motion in rest and the asymptotic behavior of solutions;

3) singularity and blow-up of weak and strong solutions;

4) vorticity and energy conservation;

5) motions of rotating fluids, or of fluids surrounding a rotating body;

6) free boundary problems;

7) maximal regularity theory and other abstract results for mathematical fluid mechanics.


For this quarter century, these topics have been playing a central role in both pure and applied mathematics

and having a great influence to the developm

ent of the functional analysis, harmonic analysis and numerical analysis whose tools make a a substantial contribution to the investigation of nonlinear partial differential equations, particularly the Navier-Stokes and the Euler equations.     

There are 24 articles in this book in which the nonlinear PDE arising in the fluid mechanics are

mainly discussed.

The authors consist of speakers and participants of the 

"International Conference on the Mathematical Fluid Dynamics"

on the occasion of Professor Yoshihiro Shibatas 60th birthday held

on March 5--9 in 2013 at old capital city Nara, Japan.


Euler equations Navier‐Stokes equations asymptotic behavior global and local well‐posedness singularity and blow‐up vorticity

Editors and affiliations

  • Herbert Amann
    • 1
  • Yoshikazu Giga
    • 2
  • Hideo Kozono
    • 3
  • Hisashi Okamoto
    • 4
  • Masao Yamazaki
    • 5
  1. 1.Universität of ZürichInstitut für MathematikZürichSwitzerland
  2. 2.University of TokyoGraduate School of Mathematical SciencesTokyoJapan
  3. 3.Department of MathematicsWaseda UniversityTokyoJapan
  4. 4.Research Institute for Mathematical SciencesKyoto University KitashirakawaKyotoJapan
  5. 5.Department of MathematicsWaseda UniversityTokyoJapan

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
  • Series Abbreviated Title Mathematical Fluid Mechanics (Birkhäuser)
  • DOI
  • Copyright Information Springer Basel 2016
  • Publisher Name Birkhäuser, Basel
  • eBook Packages Mathematics and Statistics Mathematics and Statistics (R0)
  • Hardcover ISBN 978-3-0348-0938-2
  • eBook ISBN 978-3-0348-0939-9
  • 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
  • Buy this book on publisher's site
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