On the periodic Schr\"odinger-Debye equation
Analysis of PDEs
2007-05-23 v1
Abstract
We study local and global well-posedness of the initial value problem for the Schr\"odinger-Debye equation in the \emph{periodic case}. More precisely, we prove local well-posedness for the periodic Schr\"odinger-Debye equation with subcritical nonlinearity in arbitrary dimensions. Moreover, we derive a new \emph{a priori} estimate for the norm of solutions of the periodic Schr\"odinger-Debye equation. A novel phenomena obtained as a by-product of this \emph{a priori} estimate is the global well-posedness of the periodic Schr\"odinger-Debye equation in dimensions and 3 \emph{without} any smallness hypothesis of the norm of the initial data in the ``focusing'' case.
Keywords
Cite
@article{arxiv.math/0511634,
title = {On the periodic Schr\"odinger-Debye equation},
author = {Alexander Arbieto and Carlos Matheus},
journal= {arXiv preprint arXiv:math/0511634},
year = {2007}
}