On the well-posedness problem for the derivativenonlinear Schrödinger equation Killip, Rowan Ntekoume, Maria Visan, Monica ddc:500 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 Publishers 2023 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/22067 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> eng info:eu-repo/semantics/altIdentifier/doi/10.2140/apde.2023.16.1245 info:eu-repo/semantics/altIdentifier/issn/2157-5045 info:eu-repo/semantics/altIdentifier/e-issn/1948-206X info:eu-repo/semantics/altIdentifier/arxiv/2101.12274 info:eu-repo/semantics/openAccess