Large-Data Equicontinuity for the Derivative NLS. (25th January 2022)

• Record Type: Journal Article
• Authors: Harrop-Griffiths, Benjamin; Killip, Rowan; Vişan, Monica
• Is Part Of: International mathematics research notices. Volume 2023:Number 6(2023)
• Page Start: 4601
• Page End: 4642
• Publication Date: 2022-01-25
• Subjects: Mathematics -- Periodicals; 510
• DOI: 10.1093/imrn/rnab374
• Languages: English
• ISSNs: 1073-7928

Abstract

Abstract: We consider the derivative nonlinear Schrödinger 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 also under the entire hierarchy. This allows us to remove the small-data restriction from prior conservation laws and global well-posedness results.