References & Citations
Mathematics > Analysis of PDEs
Title: Intermediate long wave equation in negative Sobolev spaces
(Submitted on 14 Nov 2023 (v1), last revised 26 Apr 2024 (this version, v2))
Abstract: We study the intermediate long wave equation (ILW) in negative Sobolev spaces. In particular, despite the lack of scaling invariance, we identify the regularity $s = -\frac 12$ as the critical regularity for ILW with any depth parameter, by establishing the following two results. (i) By viewing ILW as a perturbation of the Benjamin-Ono equation (BO) and exploiting the complete integrability of BO, we establish a global-in-time a priori bound on the $H^s$-norm of a solution to ILW for $ - \frac 12 < s < 0$. (ii) By making use of explicit solutions, we prove that ILW is ill-posed in $H^s$ for $s < - \frac 12$. Our results apply to both the real line case and the periodic case.
Submission history
From: Tadahiro Oh [view email][v1] Tue, 14 Nov 2023 13:16:39 GMT (19kb)
[v2] Fri, 26 Apr 2024 08:14:42 GMT (20kb)
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