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Zusatztext ...recommended...providing an excellent overview of the technical aspects of Navier-Stokes analysis [and] the physical effects...of rotating flows. Informationen zum Autor Jean-Yves Chemin is a Professor at the University of Paris VIBenoit Desjardins is based at the Centre of Atomic Studies centre de Bruyers le ChatelIsabelle Gallagher is a Professor at the Institut de Mathématiques de JussieuEmmanuel Greiner is based at the École Normale Superiore de Lyon Klappentext 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 fourparts, with the first part providing the physical background of the geophysical models to be analyzed. Part two is devoted to a self contained proof of the existence of weak (or strong) solutions to the imcompressible Navier-Stokes equations. Part three deals with the rapidly rotatingNavier-Stokes equations, first in the whole space, where dispersion effects are considered. The case where the domain has periodic boundary conditions is then analyzed, and finally rotating Navier-Stokes equations between two plates are studied, both in the case of periodic horizontal coordinatedand 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. Finallyspherical layers are introduced, whose study is completely open. Zusammenfassung Aimed at graduate students and researchers 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 Navier-Stokes equations are examined in both incompressible and rapidly rotating forms. Inhaltsverzeichnis 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 ...
