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arXiv · 2411.05300

Global well-posedness and equicontinuity for mKdV in modulation spaces

Saikatul Haque·Rowan Killip·Monica Visan·Yunfeng Zhang
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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 $M_p^{s,2}(\mathbb{R})$, for all $1\leq p<\infty$ and $0\leq s<3/2-1/p$. 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.

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Saikatul Haque, Rowan Killip, Monica Visan, Yunfeng Zhang. 2024-11-08. Global well-posedness and equicontinuity for mKdV in modulation spaces. https://doi.org/10.2140/paa.2025.7.615

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