Advances in Mathematical Fluid Mechanics

Contributions to Current Challenges in Mathematical Fluid Mechanics

Editors: Galdi, Giovanni P., Heywood, Malcolm I., Rannacher, Rolf (Eds.)

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About this book

This volume consists of five research articles, each dedicated to a significant topic in the mathematical theory of the Navier-Stokes equations, for compressible and incompressible fluids, and to related questions. All results given here are new and represent a noticeable contribution to the subject. One of the most famous predictions of the Kolmogorov theory of turbulence is the so-called Kolmogorov-obukhov five-thirds law. As is known, this law is heuristic and, to date, there is no rigorous justification. The article of A. Biryuk deals with the Cauchy problem for a multi-dimensional Burgers equation with periodic boundary conditions. Estimates in suitable norms for the corresponding solutions are derived for "large" Reynolds numbers, and their relation with the Kolmogorov-Obukhov law are discussed. Similar estimates are also obtained for the Navier-Stokes equation. In the late sixties J. L. Lions introduced a "perturbation" of the Navier­ Stokes equations in which he added in the linear momentum equation the hyper­ dissipative term (-Ll),Bu, f3 ~ 5/4, where Ll is the Laplace operator. This term is referred to as an "artificial" viscosity. Even though it is not physically moti­ vated, artificial viscosity has proved a useful device in numerical simulations of the Navier-Stokes equations at high Reynolds numbers. The paper of of D. Chae and J. Lee investigates the global well-posedness of a modification of the Navier­ Stokes equation similar to that introduced by Lions, but where now the original dissipative term -Llu is replaced by (-Ll)O:u, 0 S Ct < 5/4.

Table of contents (5 chapters)

  • On Multidimensional Burgers Type Equations with Small Viscosity

    Biryuk, Andrei

    Pages 1-30

  • On the Global Well-posedness and Stability of the Navier—Stokes and the Related Equations

    Chae, Dongho (et al.)

    Pages 31-51

  • The Commutation Error of the Space Averaged Navier-Stokes Equations on a Bounded Domain

    Dunca, A. (et al.)

    Pages 53-78

  • The Nonstationary Stokes and Navier-Stokes Flows Through an Aperture

    Hishida, Toshiaki

    Pages 79-123

  • Asymptotic Behavior at Infinity of Exterior Three-dimensional Steady Compressible Flow

    Leonavičienė, T. (et al.)

    Pages 125-151

Buy this book

eBook $99.00
price for USA (gross)
  • ISBN 978-3-0348-7877-7
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $149.00
price for USA
  • ISBN 978-3-7643-7104-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $129.00
price for USA
  • ISBN 978-3-0348-9606-1
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Contributions to Current Challenges in Mathematical Fluid Mechanics
Editors
  • Giovanni P. Galdi
  • Malcolm I. Heywood
  • Rolf Rannacher
Series Title
Advances in Mathematical Fluid Mechanics
Copyright
2004
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-7877-7
DOI
10.1007/978-3-0348-7877-7
Hardcover ISBN
978-3-7643-7104-3
Softcover ISBN
978-3-0348-9606-1
Series ISSN
2297-0320
Edition Number
1
Number of Pages
VIII, 152
Topics