A priori estimates for the derivative nonlinear Schr\"{o}dinger equation
Analysis of PDEs
2022-12-26 v2
Abstract
We prove low regularity a priori estimates for the derivative nonlinear Schr\"{o}dinger equation in Besov spaces with positive regularity index conditional upon small -norm. This covers the full subcritical range. We use the power series expansion of the perturbation determinant introduced by Killip--Vi\c{s}an--Zhang for completely integrable PDE. This makes it possible to derive low regularity conservation laws from the perturbation determinant.
Keywords
Cite
@article{arxiv.2007.13161,
title = {A priori estimates for the derivative nonlinear Schr\"{o}dinger equation},
author = {Friedrich Klaus and Robert Schippa},
journal= {arXiv preprint arXiv:2007.13161},
year = {2022}
}
Comments
14 pages, revised version, to appear in Funkcial. Ekvac