article published yes Benjamin Harrop-Griffiths author Rowan Killip author Monica Visan author 056daca0-b8d1-11f0-964f-f91054abf8ca 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. Oxford University Press2023 eng 1073-7928 1687-0247 2106.1333310.1093/imrn/rnab374 202364601-4642 yes Harrop-Griffiths, Benjamin, Rowan Killip, and Monica Vişan. “Large-Data Equicontinuity for the Derivative NLS.” <i>International Mathematics Research Notices</i>. Oxford University Press, 2023. <a href="https://doi.org/10.1093/imrn/rnab374">https://doi.org/10.1093/imrn/rnab374</a>. Harrop-Griffiths, B., Killip, R., &#38; Vişan, M. (2023). Large-data equicontinuity for the derivative NLS. <i>International Mathematics Research Notices</i>. Oxford University Press. <a href="https://doi.org/10.1093/imrn/rnab374">https://doi.org/10.1093/imrn/rnab374</a> B. Harrop-Griffiths, R. Killip, and M. Vişan, “Large-data equicontinuity for the derivative NLS,” <i>International Mathematics Research Notices</i>, vol. 2023, no. 6. Oxford University Press, pp. 4601–4642, 2023. Harrop-Griffiths, Benjamin, et al. “Large-Data Equicontinuity for the Derivative NLS.” <i>International Mathematics Research Notices</i>, vol. 2023, no. 6, Oxford University Press, 2023, pp. 4601–42, doi:<a href="https://doi.org/10.1093/imrn/rnab374">10.1093/imrn/rnab374</a>. Harrop-Griffiths B, Killip R, Vişan M. Large-data equicontinuity for the derivative NLS. <i>International Mathematics Research Notices</i>. 2023;2023(6):4601-4642. doi:<a href="https://doi.org/10.1093/imrn/rnab374">10.1093/imrn/rnab374</a> Harrop-Griffiths B, Killip R, Vişan M. 2023. Large-data equicontinuity for the derivative NLS. International Mathematics Research Notices. 2023(6), 4601–4642. B. Harrop-Griffiths, R. Killip, M. Vişan, International Mathematics Research Notices 2023 (2023) 4601–4642. 220722026-06-19T08:22:03Z2026-06-30T10:56:42Z