A remark on the well-posedness of the modified KdV equation in L²

2022/05/26 by Justin Forlano, Forlano, Justin · 1 citation
Mathematics · #35Q53 #37K10 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2205.13110

openalex publication_date 2022/05/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the real-valued modified KdV equation on the real line and the circle, in both the focusing and the defocusing case. By employing the method of commuting flows introduced by Killip and Vişan (2019), we prove global well-posedness in H^s for 0≤ s<\tfrac12. On the line, we show how the arguments in the recent paper by Harrop-Griffiths, Killip, and Vişan (2020) may be simplified in the higher regularity regime s≥ 0. On the circle, we provide an alternative proof of the sharp global well-posedness in L² due to Kappeler and Topalov (2005), and also extend this to the large-data focusing case.

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