Globally well and ill posedness for non-elliptic derivative Schrödinger equations with small rough data

We show that there exists sc>0sc>0 such that the cubic (quartic) non-elliptic derivative Schrödinger equations with small data in modulation spaces M2,1s(Rn) for n≥3n≥3 (n=2n=2) are globally well-posed if s≥scs≥sc, and ill-posed if s