English

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 L2L^2-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