Large-data equicontinuity for the derivative NLS

TL;DR

This paper proves that for the derivative NLS equation, the orbits of initial data that are bounded and equicontinuous in L^2 remain so under the flow and hierarchy, removing previous small-data restrictions.

Contribution

It establishes large-data equicontinuity for the derivative NLS, extending conservation laws and global well-posedness beyond small initial data.

Findings

Orbits of bounded, equicontinuous initial data stay bounded and equicontinuous.

Removes small-data restrictions from conservation laws.

Supports global well-posedness for large initial data.

Abstract

We consider the derivative NLS equation in one spatial dimension, which is known to be completely integrable. We prove that the orbits of $L^2$ bounded and equicontinuous sets of initial data remain bounded and equicontinuous, not only under this flow, but under the entire hierarchy. This allows us to remove the small-data restriction from prior conservation laws and global well-posedness results.