郝成春研究员(Prof. Chengchun Hao) - Harmonic analysis method for nonlinear evolution equations,I

郝成春的个人主页 | Chengchun HAO's Homepage

研究员、博士生导师，中国科学院数学与系统科学研究院数学研究所 | Professor, Institute of Mathematics, AMSS, CAS

Harmonic analysis method for nonlinear evolution equations,I

Baoxiang Wang, Zhaohui Huo, Chengchun Hao, Zihua Guo

World Scientific Pub Co Inc, 2011, xiv+283

Abstract:This monograph provides a comprehensive overview on a class of nonlinear evolution equations, such as nonlinear Schr？dinger 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.

Sample Chapter(s)

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

Contents:

Fourier Multiplier, Function Spaces $X_{p,q}^s$
Navier-Stokes Equation
Strichartz Estimates for Linear Dispersive Equations
Local and Global Wellposedness for Nonlinear Dispersive Equations
The Low Regularity Theory for the Nonlinear Dispersive Equations
Frequency-Uniform Decomposition Techniques
Conservations, Morawetz' Estimates of Nonlinear Schr？dinger Equations
Boltzmann Equation without Angular Cutoff

Harmonic analysis method for nonlinear evolution equations,I

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