Global dispersive estimates for defocusing nonlinear Schrodinger equations
Analysis of PDEs
2020-12-16 v3 Mathematical Physics
math.MP
Abstract
We consider the defocusing nonlinear Schr{\"o}dinger equation with a gauge invariant power-like nonlinearity. We prove global dispersive estimates in a semi-classical scaling, after rescaling the solution thanks to a suitable distorsion of the natural dispersion rate. We show a uniform bound on the modulus of the solution in some space providing compactness properties. We discuss the consequences of these estimates in the light of both scattering theory and semi-classical analysis.
Cite
@article{arxiv.1905.07915,
title = {Global dispersive estimates for defocusing nonlinear Schrodinger equations},
author = {Rémi Carles},
journal= {arXiv preprint arXiv:1905.07915},
year = {2020}
}
Comments
Several flaws whose corrections would strongly diminish the interest of these notes