Global well-posedness for the derivative nonlinear Schr\"{o}dinger equation in $H^{\frac 12} (\mathbb{R})$

TL;DR

This paper establishes the global well-posedness of the derivative nonlinear Schrödinger equation in the critical Sobolev space for initial data with mass below a specific threshold, advancing understanding of its long-term behavior.

Contribution

It proves global well-posedness in $H^{1/2}(R)$ for initial data with mass less than $4 extpi$, a significant extension in the theory of this equation.

Findings

Global well-posedness in $H^{1/2}(R)$ for mass < 4π.

Identification of the mass threshold for well-posedness.

Advancement in understanding the dynamics of the derivative NLS.

Abstract

We prove that the derivative nonlinear Schr\"{o}dinger equation is globally well-posed in $H^{\frac 12} (\mathbb{R})$ when the mass of initial data is strictly less than $4\pi$.