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Bahouri, Hajer; Chemin, Jean-Yves; Danchin, Raphaël

Fourier Analysis and Nonlinear Partial Differential Equations (Gebundene Ausgabe)


Reihe: Grundlehren der mathematischen Wissenschaften

Springer-Verlag GmbH, Springer Berlin, Januar 2011


523 S. - Sprache: Englisch - 245x166x33 mm Book

ISBN: 3642168299 EAN: 9783642168291

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.


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Produktdetails

First accessible work giving an exhaustive and up-to-date presentation of how to use Fourier analysis to study PDEs.Written by experts in the field of Fourier analysis, this work presents a self-contained state of the art of techniques with applications to different classes of PDEs.Both accessible to anyone with a good undergraduate level in analysis, as well as to experts and researchers.

Inhaltsverzeichnis

Preface.- 1. Basic analysis.- 2. Littlewood-Paley theory.- 3. Transport and transport-diffusion equations.- 4. Quasilinear symmetric systems.- 5. Incompressible Navier-Stokes system.- 6. Anisotropic viscosity.- 7. Euler system for perfect incompressible fluids.- 8. Strichartz estimates and applications to semilinear dispersive equations.- 9. Smoothing effect in quasilinear wave equations.- 10.- The compressible Navier-Stokes system.- References. - List of notations.- Index.

Kritikerstimmen

From the reviews:"This book intends to prepare the reader how to apply tools from Fourier analysis to directly solve problems arising in the theory of non linear partial differential equations. ... The presentation is well structured and easy to follow. ... This is a textbook for advanced undergraduate or beginning graduate students with a good background in real and functional analysis. ... even active researchers or mathematicians interested in the application of Fourier-analytic tools will find this book very useful." (Peter R. Massopust, Mathematical Reviews, Issue 2011 m)"The aim of the present monograph is to introduce methods from Fourier analysis, and in particular techniques based on the Littlewood-Paley decomposition, for the solution of nonlinear partial differential equations. ... The presentation is fairly self-contained and only requires a solid background in measure theory and functional analysis. It will be of value to both graduate students and researchers interested in application of Fourier analysis to partial differential equations." (G. Teschl, Monatshefte für Mathematik, Vol. 165 (3-4), March, 2012)"This book is a well-written introduction to Fourier analysis, Littlewood-Paley theory and some of their applications to the theory of evolution equations. It is suitable for readers with a solid undergraduate background in analysis. A feature that distinguishes it from other books of this sort is its emphasis on using Littlewood-Paley decomposition to study nonlinear differential equations. ... the references, historical background, and discussion of possible future developments at the end of each chapter are very convenient for its readers." (Lijing Sun, Zentralblatt MATH, Vol. 1227, 2012)


ISBN 3-642-16829-9

ISBN 978-3-642-16829-1

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Hajer;Chemin Bahouri
Fourier Analysis and Nonlinear Partial Differential Equations (Grundlehren der mathematischen Wissenschaften, Band 343) 2011
Springer,2011 Gebundene Ausgabe EAN: 9783642168291 (ISBN: 3642168299)


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