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Global well-posedness and equicontinuity for mKdV in modulation spaces

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arxiv 2411.05300 v1 pith:ZQF64NID submitted 2024-11-08 math.AP

Saikatul Haque , Rowan Killip , Monica Visan , Yunfeng Zhang This is my paper · ORCID
classification math.AP
keywords spaceswell-posednessequicontinuousglobalmodulationadmitargumentbounds
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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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  1. Well-posedness and invariant measures for complex valued modified KdV equation

    math.AP 2025-01 conditional novelty 7.0 of 10

    For the complex-valued periodic mKdV, the authors construct infinitely many invariant weighted Gaussian measures and prove unconditional well-posedness at H^s for s>4/3.

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