Global well-posedness and equicontinuity for modified Korteweg–de Vries equations in modulation spaces
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.
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Author
Haque, Saikatul;
Killip, Rowan;
Vişan, MonicaISTA;
Zhang, Yunfeng
Abstract
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.
Publishing Year
Date Published
2025-06-18
Journal Title
Pure and Applied Analysis
Publisher
Mathematical Sciences Publishers
Volume
7
Issue
3
Page
615-637
ISSN
eISSN
IST-REx-ID
Cite this
Haque S, Killip R, Vişan M, Zhang Y. Global well-posedness and equicontinuity for modified Korteweg–de Vries equations in modulation spaces. Pure and Applied Analysis. 2025;7(3):615-637. doi:10.2140/paa.2025.7.615
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. Mathematical Sciences Publishers. https://doi.org/10.2140/paa.2025.7.615
Haque, Saikatul, Rowan Killip, Monica Vişan, and Yunfeng Zhang. “ Global Well-Posedness and Equicontinuity for Modified Korteweg–de Vries Equations in Modulation Spaces.” Pure and Applied Analysis. Mathematical Sciences Publishers, 2025. https://doi.org/10.2140/paa.2025.7.615.
S. Haque, R. Killip, M. Vişan, and Y. Zhang, “ Global well-posedness and equicontinuity for modified Korteweg–de Vries equations in modulation spaces,” Pure and Applied Analysis, vol. 7, no. 3. Mathematical Sciences Publishers, pp. 615–637, 2025.
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, Saikatul, et al. “ Global Well-Posedness and Equicontinuity for Modified Korteweg–de Vries Equations in Modulation Spaces.” Pure and Applied Analysis, vol. 7, no. 3, Mathematical Sciences Publishers, 2025, pp. 615–37, doi:10.2140/paa.2025.7.615.
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