Deep-water limit of the intermediate long wave equation in L²

2023/11/14 by Andreia Chapouto, Chapouto, Andreia, Guopeng Li +5 · 3 citations
Mathematics · #35Q35 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2311.07997

openalex publication_date 2023/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We study the well-posedness issue of the intermediate long wave equation (ILW) on both the real line and the circle. By applying the gauge transform for the Benjamin-Ono equation (BO) and adapting the L² well-posedness argument for BO by Molinet and the fourth author (2012), we prove global well-posedness of ILW in L² on both the real line and the circle. In the periodic setting, this provides the first low regularity well-posedness of ILW. We then establish convergence of the ILW dynamics to the BO dynamics in the deep-water limit at the L²-level.

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• A priori bounds and equicontinuity of orbits for the intermediate long wave equation
• Low regularity well-posedness of nonlocal dispersive perturbations of Burgers' equation
• Global well-posedness for the ILW equation in H^s(\mathbbT) for s>-\frac12

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