On Schrödinger type evolution equations with non-Lipschitz coefficients

We prove results of well-posedness of the global Cauchy problem in Sobolev spaces for a class of evolution equations with real characteristics that contains an Euler– Bernoulli vibrating beam model. We consider non-Lipschitz coefficients with respect to the time variable t and study the sharp rate of their oscillations. This is coupled with some necessary decay conditions as the spatial variable x → ∞