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Unconditional deep-water limit of the intermediate long wave equation in low-regularity
Justin Forlano1, Guopeng Li1,2, Tengfei Zhao3
1School of Mathematics, The University of Edinburgh and The Maxwell Institute for the Mathematical Sciences, James Clerk Maxwell Building, The King's Buildings, Peter Guthrie Tait Road, Edinburgh, EH9 3FD UK.
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 when on the line and on the circle, where . 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.
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