Among nonlinear PDEs, dispersive and wave equations form an important class of
equations. These include the nonlinear Schrodinger equation, the nonlinear wave equation …

A BILINEAR ESTIMATE WITH APPLICATIONS TO THE KdV EQUATION 1. Introduction In this
article we continue our study of the initial v Page 1 JOURNAL OF THE AMERICAN …

We establish local well-posedness in the Sobolev space Hs with any s> 3 2 for an integrable
nonlinearly dispersive wave equation arising as a model for shallow water waves known as …

In a recent paper, Kenig, Ponce and Vega study the low regularity behavior of the focusing
nonlinear Schrödinger (NLS), focusing modified Korteweg-de Vries (mKdV), and complex …

This book was first published in 2001. It provides an introduction to Fourier analysis and
partial differential equations and is intended to be used with courses for beginning graduate …

Studied here is an initial-and boundary-value problem for the Korteweg–de Vries equation
posed on a bounded interval with nonhomogeneous boundary conditions. This particular …

1. Introduction. This is a follow-up on our work [KIMa] concerning spacetime estimates for
null forms and their relevance to the problem of optimal regularity of initial conditions for …

In this paper we prove that the one-dimensional Schrödinger equation with derivative in the
nonlinear term is globally well-posed in Hs for s>\frac12 for data small in L 2. To understand …

We prove that the one-dimensional Schrödinger equation with derivative in the nonlinear
term is globally well-posed in Hs for s> 2/3, for small L 2 data. The result follows from an …

We prove an endpoint multilinear estimate for the Xs, b spaces associated to the periodic
Airy equation. As a consequence we obtain sharp local well-posedness results for periodic …