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Perfect Incompressible Fluids
An accessible and self-contained introduction to recent advances in fluid dynamics, this book provides an authoritative account of the Euler equations for a perfect incompressible fluid. The book begins with a derivation of the Euler equations from a variational principle. It then recalls the relations on vorticity and pressure and proposes various weak formulations. The book develops the key tools for analysis: the Littlewood-Paley theory, action of Fourier multipliers on L spaces, and partial differential calculus. These techniques are used to prove various recent results concerning vortex patches or sheets; the main results include the persistence of the smoothness of the boundary of a vortex patch, even if that smoothness allows singular points, and the existence of weak solutions of the vorticity sheet type. The text also presents properties of microlocal (analytic or Gevrey) regularity of the solutions of Euler equations and links such properties to the smoothness in time of the flow of the solution vector field.
Lectures on the Analysis of Nonlinear Partial Differential Equations
This volume presents some of the most recent progress in the mathematical theory of fluid mechanics. The eight papers herein originated in a series of seminars held in 2011 at the Chinese Academy of Sciences in Beijing. Among them are Nicolas Burq on the wellposedness of the water wave problem with rough data, Jean-Yves Chemin on the wellposedness of the Navier-Stokes system, and Isabelle Gallagher on the semiclassical limit of a geostrophic system. This third volume of the series is a good reference for those working on nonlinear partial differential equations, especially as applied to fluid mechanics equations and micro-local analysis.
Fourier Analysis and Nonlinear Partial Differential Equations
In recent years, the Fourier analysis methods have expereinced a growing interest in the study of partial differential equations. In particular, those techniques based on the Littlewood-Paley decomposition have proved to be very efficient for the study of evolution equations. The present book aims at presenting self-contained, state- of- the- art models of those techniques with applications to different classes of partial differential equations: transport, heat, wave and Schrödinger equations. It also offers more sophisticated models originating from fluid mechanics (in particular the incompressible and compressible Navier-Stokes equations) or general relativity. It is either directed to anyone with a good undergraduate level of knowledge in analysis or useful for experts who are eager to know the benefit that one might gain from Fourier analysis when dealing with nonlinear partial differential equations.
Mathematical Geophysics
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.
Partial Differential Equations arising from Physics and Geometry
Presents the state of the art in PDEs, including the latest research and short courses accessible to graduate students.
Semilinear Schrodinger Equations
The nonlinear Schrodinger equation has received a great deal of attention from mathematicians, particularly because of its applications to nonlinear optics. This book presents various mathematical aspects of the nonlinear Schrodinger equation. It studies both problems of local nature and problems of global nature.
Introduction to PDEs and Waves for the Atmosphere and Ocean
Written by a leading specialist in the area of atmosphere/ocean science (AOS), the book presents an excellent introduction to this important topic. The goals of these lecture notes, based on courses presented by the author at the Courant Institute of Mathematical Sciences, are to introduce mathematicians to the fascinating and important area of atmosphere/ocean science (AOS) and, conversely, to develop a mathematical viewpoint on basic topics in AOS of interest to the disciplinary AOS community, ranging from graduate students to researchers. The lecture notes emphasize the serendipitous connections between applied mathematics and geophysical flows in the style of modern applied mathematics, ...
The Success of Apprenticeships
Apprenticeships can offer apprentices, their teacher-tutors and business apprenticeship supervisors experiences that are rich in knowledge. The Success of Apprenticeships presents the observations and opinions of 48 actors regarding apprenticeships. These testimonies recount how apprenticeships allowed them to improve their expertise, their professional practices and their organization skills. This book also examines how their interactions in the work/study process allowed them not only to develop the skills of apprentices, but also the skills of those who accompanied them – the teacher-tutors and the business apprenticeships supervisors. The creation of an authentic community of apprentices subscribes to the formation of an ecosystem of learning, in which each individual harvests fruits in terms of the development of their personal abilities.
Function Spaces and Partial Differential Equations
This is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour. The strength of the book primarily lies in its clear and detailed explanations, scope and coverage, highlighting and presenting deep and profound inter-connections between different related and seemingly unrelated disciplines within classical and modern mathematics and above all the extensive collection of examples, worked-out and hinted exercises. There are well over 700 exercises of varying level leading the reader from the basics to the most advanced levels and frontiers of research. The book can be used either for independent study or for a year-long graduate level course. In fact it has its origin in a year-long graduate course taught by the author in Oxford in 2004-5 and various parts of it in other institutions later on. A good number of distinguished researchers and faculty in mathematics worldwide have started their research career from the course that formed the basis for this book.
The Black Book of Communism
This international bestseller plumbs recently opened archives in the former Soviet bloc to reveal the accomplishments of communism around the world. The book is the first attempt to catalogue and analyse the crimes of communism over 70 years.
