| Title: |
Intermediate long wave equation in negative Sobolev spaces. |
| Authors: |
Chapouto, Andreia1 (AUTHOR), Forlano, Justin1 (AUTHOR), Li, Guopeng2 (AUTHOR), Oh, Tadahiro1 (AUTHOR), Pilod, Didier3 (AUTHOR) |
| Source: |
Proceedings of the American Mathematical Society, Series B. 9/12/2024, Vol. 11, p452-468. 17p. |
| Subject Terms: |
*SOBOLEV spaces, *WAVE equation, *PERTURBATION theory, *A priori, *EQUATIONS |
| 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. [ABSTRACT FROM AUTHOR] |
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