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- Title
Intermediate long wave equation in negative Sobolev spaces.
- Authors
Chapouto, Andreia; Forlano, Justin; Li, Guopeng; Oh, Tadahiro; Pilod, Didier
- 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.
- Subjects
SOBOLEV spaces; WAVE equation; PERTURBATION theory; A priori; EQUATIONS
- Publication
Proceedings of the American Mathematical Society, Series B, 2024, Vol 11, p452
- ISSN
2330-1511
- Publication type
Article
- DOI
10.1090/bproc/206