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Global well-posedness and
equicontinuity for modified Korteweg–de Vries equations in
modulation spaces
Saikatul Haque, Rowan Killip, Monica Vişan and Yunfeng Zhang |
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Vol. 7 (2025), No. 3, 615–637
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Abstract |
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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 , for all and . 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. |
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Keywords
mKdV, modulation spaces, global well-posedness
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Mathematical Subject Classification
Primary: 35Q53, 35Q55
Secondary: 37K10
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Milestones
Received: 22 November 2024
Revised: 13 March 2025
Accepted: 4 May 2025
Published: 18 June 2025
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Authors |
| Saikatul Haque | |
| Department of Mathematics University of California Los Angeles, CA United States |
Harish-Chandra Research
Institute Allahabad India |
| Rowan Killip | |
| Department of Mathematics University of California Los Angeles, CA United States |
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| Monica Vişan | |
| Department of Mathematics University of California Los Angeles, CA United States |
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| Yunfeng Zhang | |
| Department of Mathematical
Sciences University of Cincinnati Cincinnati, OH United States |
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| © 2025 MSP (Mathematical Sciences Publishers). |
