Work

Unconditional deep-water limit of the intermediate long wave equation in low-regularity

Year: 2025

Type: article

Abstract: In this paper, we establish the unconditional deep-water limit of the intermediate long wave equation (ILW) to the Benjamin-Ono equation (BO) in low-regularity Sobolev spaces on both the real line and the circle. Our main tool is new unconditional uniqueness results for ILW in $$H^s$$ H s when $$s_0 s 0 < s ≤ 1 4 on the line and $$s_0 s 0 < s < 1 2 on the circle, where $$s_0 = 3-\sqrt{33/4}\approx 0.1277$$ s 0 = 3 - 33 / 4 ≈ 0.1277 . Here, we adapt the strategy of Moşincat-Pilod (Pure Appl Anal 5:285–322, 2023) for BO to the setting of ILW by viewing ILW as a perturbation of BO and making use of the smoothing property of the perturbation term.

Source: Nonlinear Differential Equations and Applications NoDEA

DOI: 10.1007/s00030-025-01037-7

Authors: Justin Forlano, Guopeng Li, Tengfei Zhao

Institutions: Maxwell Institute for Mathematical Sciences, University of Edinburgh, Beijing Institute of Technology, University of Science and Technology Beijing

Language: English

Topic: Advanced Mathematical Physics Problems

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: National Natural Science Foundation of China, China Scholarship Council, European Research Council