Fourier Analysis and Nonlinear Partial Dif...

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Beschreibung

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.

Zusammenfassung

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.

Includes supplementary material: [...]

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.

Details

Erscheinungsjahr:	2013
Fachbereich:	Analysis
Genre:	Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Reihe:	Grundlehren der mathematischen Wissenschaften
Inhalt:	xvi 524 S.
ISBN-13:	9783642266577
ISBN-10:	3642266576
Sprache:	Englisch
Ausstattung / Beilage:	Paperback
Einband:	Kartoniert / Broschiert
Autor:	Bahouri, Hajer Danchin, Raphaël Chemin, Jean-Yves
Hersteller:	Springer-Verlag GmbH Springer Berlin Heidelberg Grundlehren der mathematischen Wissenschaften
Maße:	235 x 155 x 29 mm
Von/Mit:	Hajer Bahouri (u. a.)
Erscheinungsdatum:	25.02.2013
Gewicht:	0,809 kg

Artikel-ID: 106040423