article published yes Rowan Killip author Maria Ntekoume author Monica Visan author 056daca0-b8d1-11f0-964f-f91054abf8ca We consider the derivative nonlinear Schrödinger equation in one space dimension, posed both on the line and on the circle. This model is known to be completely integrable and L^2-critical with respect to scaling. We first discuss whether ensembles of orbits with L^2-equicontinuous initial data remain equicontinuous under evolution. We prove that this is true under the restriction M(q)=∫∣∣q∣∣2<4π. We conjecture that this restriction is unnecessary. Further, we prove that the problem is globally well posed for initial data in H1∕6 under the same restriction on M. Moreover, we show that this restriction would be removed by a successful resolution of our equicontinuity conjecture. Mathematical Sciences Publishers2023 eng 2157-5045 1948-206X 2101.1227410.2140/apde.2023.16.1245 1651245-1270 yes Killip, Rowan, Maria Ntekoume, and Monica Vişan. “On the Well-Posedness Problem for the Derivativenonlinear Schrödinger Equation.” <i>Analysis &#38; PDE</i>. Mathematical Sciences Publishers, 2023. <a href="https://doi.org/10.2140/apde.2023.16.1245">https://doi.org/10.2140/apde.2023.16.1245</a>. R. Killip, M. Ntekoume, and M. Vişan, “On the well-posedness problem for the derivativenonlinear Schrödinger equation,” <i>Analysis &#38; PDE</i>, vol. 16, no. 5. Mathematical Sciences Publishers, pp. 1245–1270, 2023. Killip, R., Ntekoume, M., &#38; Vişan, M. (2023). On the well-posedness problem for the derivativenonlinear Schrödinger equation. <i>Analysis &#38; PDE</i>. Mathematical Sciences Publishers. <a href="https://doi.org/10.2140/apde.2023.16.1245">https://doi.org/10.2140/apde.2023.16.1245</a> Killip R, Ntekoume M, Vişan M. On the well-posedness problem for the derivativenonlinear Schrödinger equation. <i>Analysis &#38; PDE</i>. 2023;16(5):1245-1270. doi:<a href="https://doi.org/10.2140/apde.2023.16.1245">10.2140/apde.2023.16.1245</a> Killip, Rowan, et al. “On the Well-Posedness Problem for the Derivativenonlinear Schrödinger Equation.” <i>Analysis &#38; PDE</i>, vol. 16, no. 5, Mathematical Sciences Publishers, 2023, pp. 1245–70, doi:<a href="https://doi.org/10.2140/apde.2023.16.1245">10.2140/apde.2023.16.1245</a>. R. Killip, M. Ntekoume, M. Vişan, Analysis &#38; PDE 16 (2023) 1245–1270. Killip R, Ntekoume M, Vişan M. 2023. On the well-posedness problem for the derivativenonlinear Schrödinger equation. Analysis &#38; PDE. 16(5), 1245–1270. 220672026-06-19T08:15:32Z2026-06-30T07:20:56Z