1. Fourier multiplier, function space [symbol]. 1.1. Schwartz space, tempered distribution,
Fourier transform. 1.2. Fourier multiplier on L [symbol]. 1.3. Dyadic decomposition, Besov …

2. Symmetries 2.1. Hamiltonian formulation 2.2. The symmetries 2.3. Group therapy 2.4.
Complete integrability 3. The local theory 3.1. Dispersive and Strichartz inequalities 3.2. The …

We consider the focusing energy-critical nonlinear Schr\" odinger equation $ iu_t+\Delta u=-|
u|^{4\over {d-2}} u $ in dimensions $ d\geq 5$. We prove that if a maximal-lifespan solution …

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 …

In this paper we prove that the defocusing, $ d $-dimensional mass critical nonlinear
Schrödinger initial value problem is globally well-posed and solutions scatter for $ u_ {0}\in …

In this paper we prove that the focusing, d-dimensional mass critical nonlinear Schrödinger
initial value problem is globally well-posed and scattering for u 0∈ L 2 (R d),‖ u 0‖ L 2 (R …

We show scattering versus blow-up dichotomy below the ground state energy for the
focusing nonlinear Klein–Gordon equation, in the spirit of Kenig and Merle for the H 1 critical …

The theory of linear dispersive equations predicts that waves should spread out and
disperse over time. However, it is a remarkable phenomenon, observed both in theory and …

The purpose of this work is to study the 3D focusing inhomogeneous nonlinear Schrödinger
equation iu t+ Δ u+| x|− b| u| 2 u= 0, where 0< b< 1/2. Let Q be the ground state solution of …

We consider the focusing L 2-critical half-wave equation in one space dimension, i\partial_t
u= D u-| u|^ 2 u, where D denotes the first-order fractional derivative. Standard arguments …