Key points are not available for this paper at this time.
We establish that the Cauchy problem for the Benjamin--Ono equation and for a rather general class of nonlinear dispersive equations with dispersion slightly weaker than that of the Korteweg--de Vries equation cannot be solved by an iteration scheme based on the Duhamel formula. As a consequence, the flow map fails to be smooth.
Molinet et al. (Mon,) studied this question.