[{"article_type":"original","issue":"5","doi":"10.2140/apde.2023.16.1245","abstract":[{"text":"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 \r\nM(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.","lang":"eng"}],"day":"12","date_published":"2023-08-12T00:00:00Z","oa":1,"author":[{"full_name":"Killip, Rowan","first_name":"Rowan","last_name":"Killip"},{"full_name":"Ntekoume, Maria","first_name":"Maria","last_name":"Ntekoume"},{"first_name":"Monica","full_name":"Visan, Monica","id":"056daca0-b8d1-11f0-964f-f91054abf8ca","last_name":"Visan"}],"arxiv":1,"ddc":["500"],"extern":"1","citation":{"short":"R. Killip, M. Ntekoume, M. Vişan, Analysis &#38; PDE 16 (2023) 1245–1270.","ama":"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>","mla":"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>.","ieee":"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.","ista":"Killip R, Ntekoume M, Vişan M. 2023. On the well-posedness problem for the derivativenonlinear Schrödinger equation. Analysis &#38; PDE. 16(5), 1245–1270.","chicago":"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>.","apa":"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>"},"article_processing_charge":"No","publisher":"Mathematical Sciences Publishers","title":"On the well-posedness problem for the derivativenonlinear Schrödinger equation","das_tickbox":"1","has_accepted_license":"1","intvolume":"        16","year":"2023","date_created":"2026-06-19T08:15:32Z","publication_identifier":{"issn":["2157-5045"],"eissn":["1948-206X"]},"external_id":{"arxiv":["2101.12274"]},"type":"journal_article","OA_place":"publisher","scopus_import":"1","publication":"Analysis & PDE","mathsc":["35Q55"],"language":[{"iso":"eng"}],"_id":"22067","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Published Version","page":"1245-1270","quality_controlled":"1","status":"public","date_updated":"2026-06-30T07:20:56Z","main_file_link":[{"open_access":"1","url":"https://doi.org/10.2140/apde.2023.16.1245"}],"tmp":{"name":"Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)","image":"/images/cc_by.png","short":"CC BY (4.0)","legal_code_url":"https://creativecommons.org/licenses/by/4.0/legalcode"},"OA_type":"diamond","publication_status":"published","month":"08","volume":16}]