Since the 1980s, Fourier analysis methods have become of ever greater interest in the study
of linear and nonlinear partial differential equations. In particular, techniques based on …

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 …

These notes are based on a course I gave at UCLA in the fall of 1994. I tried to make the
course self-contained, presenting as background basic facts about the solution of the linear …

We prove existence and scattering results for semilinear wave equations with low regularity
data. We also determine the minimal regularity that is needed to ensure local existence and …

Aimed at graduate students, researchers and academics in mathematics, engineering,
oceanography, meteorology and mechanics, this text provides a detailed introduction to the …

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 …

This is the main paper in a sequence in which we give a complete proof of the bounded L^ 2
L 2 curvature conjecture. More precisely we show that the time of existence of a classical …

Sharp Local Well-Posedness Results for the Nonlinear Wave Equation Page 1 Annals of
Mathematics, 162 (2005), 291-366 Sharp local well-posedness results for the nonlinear wave …

Dans cet article, notre but est de résoudre des équations d'ondes quasilinéaires pour des
données initiales moins régulières que ce qu'imposent les méthodes d'énergie. Ceci impose …