On the well-posedness theory for higher-order (d)NLS hierarchy equations

by Dr Joseph Adams (Heinrich-Heine-Universität Düsseldorf)

Friday Jun 26, 2026, 2:15 PM → 3:45 PM Europe/Berlin

Endenicher Allee 60, Seminarraum 0.011 (Mathezentrum)

Abstract:

Complete integrability of dispersive PDEs has become a central property in the well-posedness and stability analysis of PDEs that possess this property, usually yielding an infinite number of conserved quantities and often explicit families of solutions available. Classical examples of such equations are the cubic nonlinear Schrödinger (NLS) equation and its close relative the derivative nonlinear Schrödinger (dNLS) equation. 

With both of these equations there are associated, higher-order, PDEs that are derived from their conservation laws - so called integrable hierarchies. In this talk we review the recent developments in the well-posedness theory of equations in these hierarchies, while not explicitly relying on their complete integrability. We will be covering said equation's derivation, (multilinear refinements of) Strichartz estimates leading to low-regularity well-posedness, as well as complementary ill-posedness results establishing optimality. We conclude with a discussion of some open questions related to the presented material.