We prove that the initial value problem associated to a perturbation of the
Benjamin-Ono equation or Chen-Lee equation ut+uux+βHuxx+η(Hux−uxx)=0, where x∈T,
t>0, η>0 and H denotes the usual Hilbert transform, is
locally and globally well-posed in the Sobolev spaces Hs(T) for any
s>−21. We also prove some ill-posedness issues when s<−1.Comment: 15 page