Intermediate long wave equation in negative Sobolev spaces
Résumé
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 = −1/2 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 −1/2