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.

arXiv comment14 pages, revised version, to appear in Funkcial. Ekvac

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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