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

We make a synthetic exposition of the generalized Strichartz inequalities for the wave
equation obtained in [6] together with the limiting cases recently obtained in [13] with as …

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 …

This work is devoted to the description of bounded energy sequences of solutions to the
equation (1)□ u+| u| 4= 0 in [inline-graphic xmlns: xlink=" http://www. w3. org/1999/xlink" …

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 …

We obtain global well-posedness, scattering, and global L_t,x^10 spacetime bounds for
energy-class solutions to the quintic defocusing Schrödinger equation in R^1+3, which is …

This volume contains notes of the lectures given at the Courant Institute and a DMV-Seminar
at Oberwolfach. The focus is on the recent work of the authors on semilinear wave equations …

We study the energy-critical focusing non-linear wave equation, with data in the energy
space, in dimensions 3, 4 and 5. We prove that for Cauchy data of energy smaller than the …

Consider the energy-critical focusing wave equation in odd space dimension $ N\geq 3$.
The equation has a nonzero radial stationary solution $ W $, which is unique up to scaling …

In this article we prove that the defocusing, cubic nonlinear Schrödinger initial value problem
is globally well posed and scattering for u 0∈ L 2 (R 2). The proof uses the bilinear …