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