| Reviews |
| - '...recommended...providing an excellent overview of the technical aspects of Navier-Stokes analysis [and] the physical effects...of rotating flows.' - Fluid Mechanics, Volume 585
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| Description | | - Aimed at graduate students, researchers and academics in mathematics, engineering, oceanography, meteorology and mechanics.
- Provides the mathematical basis for many important large-scale phenomena
- Rigorous proofs throughout
| Aimed at graduate students, researchers and academics in mathematics, engineering, oceanography, meteorology and mechanics, this text provides a detailed introduction to the physical theory of rotating fluids, a significant part of geophysical fluid dynamics. The text is divided into four parts, with the first part providing the physical background of the geophysical models to be analysed.
Part II is devoted to a self contained proof of the existence of weak (or strong) solutions to the incompressible Navier-Stokes equations. Part III deals with the rapidly rotating Navier-Stokes equations, first in the whole space, where dispersion effects are considered. The case where the domain has periodic boundary conditions is then analysed, and finally rotating Navier-Stokes equations
between two plates are studied, both in the case of periodic horizontal coordinates and those in R². In Part IV the stability of Ekman boundary layers, and boundary layer effects in magnetohydrodynamics and quasigeostrophic equations are discussed. The boundary layers which appear near vertical walls are presented and formally linked with the classical Prandlt equations. Finally spherical
layers are introduced, whose study is completely open.
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Readership: Graduate students, researchers and academics in mathematics, engineering, oceanography, meteorology and mechanics
| Contents |
Preface
General Introduction
On the Navier-Stokes Equations
1.
Some Elements of Functional Analysis
2.
Weak Solutions of the Navier-Stokes Equations
3.
Stability of the Navier-Stokes Equations
4.
References and Remarks on the Navier-Stokes Equations
Rotating Fluids
5.
Dispersive Cases
6.
The Periodic Case
7.
Ekman Boundary Layers for Rotating Fluids
8.
References and Remarks on Rotating Fluids
Perspectives
9.
Stability of Horizontal Boundary Layers
10.
Other Systems
11.
Vertical Layers
12.
Other Layers
References
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| Authors, editors,
and contributors |
Jean-Yves Chemin, Laboratoire J.-L. Lions, University of Paris 6,
Benoit Desjardins, Centre of Atomic Studies,
Isabelle Gallagher, Institut de Mathematiques de Jussieu, University of Paris 7, and
Emmanuel Grenier, Ecole Normale Superiore de Lyon
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The specification in this catalogue, including without
limitation price, format, extent, number of illustrations,
and month of publication, was as accurate as
possible at the time the catalogue was compiled.
Occasionally, due to the nature of some contractual restrictions, we
are unable to ship a specific product to a particular territory.
Jacket images are provisional and liable to change before publication.
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