Large-Data Equicontinuity for the Derivative NLS. (25th January 2022) - Harrop-Griffiths, Benjamin; Killip, Rowan; Vişan, Monica
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.