We study the local existence of strong solutions for the cubic nonlinear wave equation with
data in H s (M), s< 1/2, where M is a three dimensional compact Riemannian manifold. This …

We consider the cubic nonlinear Schrödinger equation posed on the spatial domain R× Td.
We prove modified scattering and construct modified wave operators for small initial and …

We consider the Cauchy problem of the cubic nonlinear Schrödinger equation (NLS) $:
i\partial _t u+\Delta u=\pm| u|^{2} u $ on $\mathbb {R}^ d $, $ d\geq 3$, with random initial …

This work can be seen as a continuation of a series of papers due to N. Burq, N. Tzvetkov
and the first author [4, 5, 6, 7]—see also [10] for a survey—, devoted to the influence of the …

A refined trilinear Strichartz estimate for solutions to the Schrödinger equation on the flat
rational torus T 3 is derived. By a suitable modification of critical function space theory this is …

In [12], we constructed and proved the invariance of a Gibbs measure associated to the sub-
cubic, focusing or defocusing Nonlinear Schrödinger equation (NLS) on the disc of the plane …

We estimate the L p-norm (2≤ p≤+∞) of the restriction to a curve of the eigenfunctions of
the Laplace-Beltrami operator on a Riemannian surface. If the curve is a geodesic, we show …

The purpose of this work is twofold. First we construct Gibbs measures and prove their
invariance by the flow of the nonlinear (focusing and defocusing) Schrödinger equations …

We introduce a randomization of a function on ℝ d R^ d that is naturally associated to the
Wiener decomposition and, intrinsically, to the modulation spaces. Such randomized …

The energy-critical defocusing NLS on T3 Page 1 THE ENERGY-CRITICAL DEFOCUSING
NLS ON T3 ALEXANDRU D. IONESCU and BENOIT PAUSADER Abstract We prove global …