Smoothing properties of some weak solutions of the Benjamin-Ono equation (Q803420)

Weak solutions corresponding to initial data in \(H^{n/2}({\mathbb{R}})\), for \(n=2\) or 3, of the Benjamin-Ono equation are shown to exhibit a local smoothing effect in the spatial variable of 1/2 a derivative, almost everywhere in time. Similar results are shown to hold true for the intermediate long wave equation and Smith's equation.