Sharp weights in the Cauchy problem for nonlinear Schrodinger equations with potential
Analysis of PDEs
2020-12-16 v3 Mathematical Physics
math.MP
Abstract
We review different properties related to the Cauchy problem for the (nonlinear) Schrodinger equation with a smooth potential. For energy-subcritical nonlinearities and at most quadratic potentials, we investigate the necessary decay in space in order for the Cauchy problem to be locally (and globally) well-posed. The characterization of the minimal decay is different in the case of super-quadratic potentials.
Cite
@article{arxiv.1409.5759,
title = {Sharp weights in the Cauchy problem for nonlinear Schrodinger equations with potential},
author = {Rémi Carles},
journal= {arXiv preprint arXiv:1409.5759},
year = {2020}
}
Comments
8 pages, Corollary 3.5 is now a bit more general