We prove that the initial value problem associated to a perturbation of the Benjamin-Ono equation or Chen-Lee equation u t + uu x + β Hu xx + ( Hu x - u xx ) = 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 H s (T) for any s > - ½. We also prove some ill-posedness issues when s < -1.
