Fourier analysis and nonlinear partial differential equations

✍ Scribed by Hajer Bahouri, Jean-Yves Chemin, Raphaël Danchin (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 2011
• Tongue: English
• Leaves: 540
• Series: Grundlehren der mathematischen Wissenschaften 343
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter....Pages I-XV
Basic Analysis....Pages 1-50
Littlewood–Paley Theory....Pages 51-121
Transport and Transport-Diffusion Equations....Pages 123-167
Quasilinear Symmetric Systems....Pages 169-202
The Incompressible Navier–Stokes System....Pages 203-243
Anisotropic Viscosity....Pages 245-289
Euler System for Perfect Incompressible Fluids....Pages 291-333
Strichartz Estimates and Applications to Semilinear Dispersive Equations....Pages 335-387
Smoothing Effect in Quasilinear Wave Equations....Pages 389-428
The Compressible Navier–Stokes System....Pages 429-496
Back Matter....Pages 497-523

✦ Subjects

Analysis; Partial Differential Equations