article published yes Saikatul Haque author Rowan Killip author Monica Visan author 056daca0-b8d1-11f0-964f-f91054abf8ca Yunfeng Zhang author We establish global well-posedness for both the defocusing and focusing complex-valued modified Korteweg–de Vries equations on the real line in modulation spaces Ms,2p (R), for all 1 p < 1 and 0 s < 3/2 − 1/p. We will also show that such solutions admit global-in-time bounds in these spaces and that equicontinuous sets of initial data lead to equicontinuous ensembles of orbits. Indeed, such information forms a crucial part of our well-posedness argument. Mathematical Sciences Publishers2025 eng 2578-5893 2578-5885 2411.0530010.2140/paa.2025.7.615 73615-637 yes 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> S. Haque, R. Killip, M. Vişan, Y. Zhang, Pure and Applied Analysis 7 (2025) 615–637. 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>. 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. 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> 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>. 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. 220212026-06-19T07:30:23Z2026-06-19T10:16:14Z