A remark on global well-posedness of the derivative nonlinear Schr\"odinger equation on the circle

TL;DR

This paper proves the global well-posedness of the derivative nonlinear Schrödinger equation on the circle for initial data with mass less than 4π, extending Wu's argument to the periodic setting and showing the threshold's independence from spatial periods.

Contribution

It adapts Wu's recent argument to the periodic setting to establish global well-posedness of the derivative NLS on the circle with a mass threshold independent of spatial periods.

Findings

Global well-posedness in H^1(T) for mass < 4π

Mass threshold is independent of spatial periods

Extension of Wu's argument to periodic setting

Abstract

In this note, we consider the derivative nonlinear Schr\"odinger equation on the circle. In particular, by adapting Wu's recent argument to the periodic setting, we prove its global well-posedness in $H^1(\mathbb T)$, provided that the mass is less than $4\pi$. Moreover, this mass threshold is independent of spatial periods.