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arXiv · 2007.13161

A priori estimates for the derivative nonlinear Schr\"{o}dinger equation

Friedrich Klaus·Robert Schippa
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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 $L^2$-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.

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Friedrich Klaus, Robert Schippa. 2020-07-26. A priori estimates for the derivative nonlinear Schr\"{o}dinger equation. https://doi.org/10.1619/fesi.65.329

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