Introduction to Nonlinear Dispersive Equations

The aim of this textbook is to introduce the theory of nonlinear dispersive equations to graduate students in a constructive way. The first three chapters are dedicated to preliminary material, such as Fourier transform, interpolation theory and Sobolev spaces. The authors then proceed to use the linear Schr&oumlet;dinger equation to describe properties enjoyed by general dispersive equations. This information is then used to treat local and global well-posedness for the semi-linear Schr&oumlet;dinger equations. The end of each chapter contains recent developments and open problems, as well as exercises.