{"OA_type":"green","main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2411.05300"}],"status":"public","publication_identifier":{"issn":["2578-5893"],"eissn":["2578-5885"]},"day":"18","article_processing_charge":"No","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","external_id":{"arxiv":["2411.05300"]},"publication_status":"published","extern":"1","intvolume":"         7","doi":"10.2140/paa.2025.7.615","volume":7,"year":"2025","publication":"Pure and Applied Analysis","scopus_import":"1","article_type":"original","date_published":"2025-06-18T00:00:00Z","issue":"3","date_created":"2026-06-19T07:30:23Z","title":" Global well-posedness and equicontinuity for modified Korteweg–de Vries equations in modulation spaces","author":[{"first_name":"Saikatul","full_name":"Haque, Saikatul","last_name":"Haque"},{"first_name":"Rowan","full_name":"Killip, Rowan","last_name":"Killip"},{"last_name":"Visan","id":"056daca0-b8d1-11f0-964f-f91054abf8ca","full_name":"Visan, Monica","first_name":"Monica"},{"last_name":"Zhang","full_name":"Zhang, Yunfeng","first_name":"Yunfeng"}],"oa_version":"Preprint","quality_controlled":"1","publisher":"Mathematical Sciences Publishers","language":[{"iso":"eng"}],"date_updated":"2026-06-19T10:16:14Z","arxiv":1,"OA_place":"repository","abstract":[{"lang":"eng","text":"We establish global well-posedness for both the defocusing and\r\nfocusing complex-valued modified Korteweg–de Vries equations on the real line\r\nin modulation spaces Ms,2p (R), for all 1 \u0014 p < 1 and 0 \u0014 s < 3/2 − 1/p. We\r\nwill also show that such solutions admit global-in-time bounds in these spaces\r\nand that equicontinuous sets of initial data lead to equicontinuous ensembles\r\nof orbits. Indeed, such information forms a crucial part of our well-posedness\r\nargument."}],"_id":"22021","month":"06","citation":{"ieee":"S. Haque, R. Killip, M. Vişan, and Y. Zhang, “ Global well-posedness and equicontinuity for modified Korteweg–de Vries equations in modulation spaces,” <i>Pure and Applied Analysis</i>, vol. 7, no. 3. Mathematical Sciences Publishers, pp. 615–637, 2025.","mla":"Haque, Saikatul, et al. “ Global Well-Posedness and Equicontinuity for Modified Korteweg–de Vries Equations in Modulation Spaces.” <i>Pure and Applied Analysis</i>, vol. 7, no. 3, Mathematical Sciences Publishers, 2025, pp. 615–37, doi:<a href=\"https://doi.org/10.2140/paa.2025.7.615\">10.2140/paa.2025.7.615</a>.","ama":"Haque S, Killip R, Vişan M, Zhang Y.  Global well-posedness and equicontinuity for modified Korteweg–de Vries equations in modulation spaces. <i>Pure and Applied Analysis</i>. 2025;7(3):615-637. doi:<a href=\"https://doi.org/10.2140/paa.2025.7.615\">10.2140/paa.2025.7.615</a>","chicago":"Haque, Saikatul, Rowan Killip, Monica Vişan, and Yunfeng Zhang. “ Global Well-Posedness and Equicontinuity for Modified Korteweg–de Vries Equations in Modulation Spaces.” <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers, 2025. <a href=\"https://doi.org/10.2140/paa.2025.7.615\">https://doi.org/10.2140/paa.2025.7.615</a>.","ista":"Haque S, Killip R, Vişan M, Zhang Y. 2025.  Global well-posedness and equicontinuity for modified Korteweg–de Vries equations in modulation spaces. Pure and Applied Analysis. 7(3), 615–637.","short":"S. Haque, R. Killip, M. Vişan, Y. Zhang, Pure and Applied Analysis 7 (2025) 615–637.","apa":"Haque, S., Killip, R., Vişan, M., &#38; Zhang, Y. (2025).  Global well-posedness and equicontinuity for modified Korteweg–de Vries equations in modulation spaces. <i>Pure and Applied Analysis</i>. Mathematical Sciences Publishers. <a href=\"https://doi.org/10.2140/paa.2025.7.615\">https://doi.org/10.2140/paa.2025.7.615</a>"},"type":"journal_article","oa":1,"page":"615-637"}