Fourier Analysis and Nonlinear Partial Differential Equations

• Main Authors: Bahouri, Hajer (Author), Chemin, Jean-Yves (Author), Danchin, Raphaël (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2011.
• Series: Grundlehren der mathematischen Wissenschaften, A Series of Comprehensive Studies in Mathematics, 343
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Partial differential equations.; Analysis.; 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 a...

Table of Contents:

• 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.