Description
Book SynopsisThis monograph provides a comprehensive overview on a class of nonlinear evolution equations, such as nonlinear Schrödinger 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.
Table of ContentsFourier Multiplier, Function Spaces; 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 Method; Conservations, Morawetz' Inequalities of NLS; Boltzmann Equation without Angular Cutoff.
