An Introduction to Rotating Fluids and the Navier-Stokes Equations
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Mathematical Geophysics by Jean-Yves Chemin
Book DescriptionAimed 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 R^2. 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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Book DetailsISBN: 9780198571339
(240mm x 160mm x 20mm)
Imprint: Clarendon Press
Publisher: Oxford University Press
Publish Date: 13-Apr-2006
Country of Publication: United Kingdom
Books By Author Jean-Yves Chemin
Fourier Analysis and Nonlinear Partial Differential Equations, Paperback (February 2013)
Recent years have seen a growth in interest in using partial differential equations in methods of Fourier analysis. This monograph sets out state-of-the-art models of these techniques as applied to transport, heat, wave, and Schrodinger equations.
Perfect Incompressible Fluids, Hardback (September 1998)» View all books by Jean-Yves Chemin
This book offers an authoritative account of various mathematical developments in fluid mechanics, offering a self contained presentation of the theory of Euler equations describing a perfect incompressible fluid. In the OXFORD LECTURE SERIES IN MATHEMATICS AND ITS APPLICATIONS series.
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Author Biography - Jean-Yves Chemin
Jean-Yves Chemin is a Professor at the University of Paris VI Benoit Desjardins is based at the Centre of Atomic Studies centre de Bruyers le Chatel Isabelle Gallagher is a Professor at the Institut de Mathematiques de Jussieu Emmanuel Greiner is based at the Ecole Normale Superiore de Lyon
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