Global well-posedness and equicontinuity for mKdV in modulation spaces

2024/11/08 by Haque, Saikatul, Killip, Rowan, Visan, Monica +1 · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.05300

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(ℝ), for all 1≤ p<∞ 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.

Cited by

• Growth of Fourier--Lebesgue norms for mKdV
• A priori bounds and equicontinuity of orbits for the intermediate long wave equation

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