Baoxiang Wang (Peking University, China),

Zhaohui Huo (Chinese Academy of Sciences, China),

Chengchun Hao (Chinese Academy of Sciences, China),

Zihua Guo (Peking University, China)

ISBN: 978-981-4360-73-9 (hardcover)

       This monograph provides a comprehensive overview on a class of nonlinear evolution equations, such as nonlinear Schrodinger equations, nonlinear Klein–Gordon equations, KdV equations as well as Navier–Stokes equations and Boltzmann equations. The global wellposedness to the Cauchy problem for those equations is systematically studied by using the harmonic analysis methods.

     This book is self-contained and may also be used as an advanced textbook by graduate students in analysis and PDE subjects and even ambitious undergraduate students.

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Sample Chapter(s)

Chapter 1: Fourier multiplier,function space $X^s_{p,q}$ (371 KB)

Readership: Graduate students and researchers interested in analysis and PDE.

Contents

1. Fourier Multiplier, Function Spaces $X^s_{p,q}$

2. Navier–Stokes Equation

3. Strichartz Estimates for Linear Dispersive Equations

4. Local and Global Wellposedness for Nonlinear Dispersive Equations

5. The Low Regularity Theory for the Nonlinear Dispersive Equations

6. Frequency-Uniform Decomposition Techniques

7. Conservations, Morawetz' Estimates of Nonlinear Schrodinger Equations

8. Boltzmann Equation without Angular Cutoff