A priori estimates for the derivative nonlinear Schrödinger equation

Abstract

We prove low regularity a priori estimates for the derivative nonlinear Schrodinger 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–Visan–Zhang for completely integrable PDE. This makes it possible to derive low regularity conservation laws from the perturbation determinant.