A priori estimates for the derivative nonlinear Schrödinger equation

Abstract

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

14 pages, revised version, to appear in Funkcial. Ekvac

References in corpus (2)

• Low regularity local well-posedness of the Derivative Nonlinear Schrödinger Equation with periodic initial data
• $H^s$ Bounds for the Derivative Nonlinear Schrödinger Equation

Cited by in corpus (3)

• On the well-posedness problem for the derivative nonlinear Schrödinger equation
• On the global well-posedness of the Calogero-Sutherland derivative nonlinear Schrödinger equation
• Well-posedness for the NLS hierarchy