Fourier Analysis and Nonlinear Partial Differential Equations

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Springer Science & Business Media, Jan 3, 2011 - Mathematics - 524 pages

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 SchrŲdinger 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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Contents

Basic Analysis
1
LittlewoodPaley Theory
51
Transport and TransportDiffusion Equations
123
Quasilinear Symmetric Systems
168
The Incompressible NavierStokes System
203
Anisotropic Viscosity
245
Euler System for Perfect Incompressible Fluids
290
Strichartz Estimates and Applications to Semilinear Dispersive Equations
335
Smoothing Effect in Quasilinear Wave Equations
388
The Compressible NavierStokes System
429
References
497
List of Notations
517
Index
520
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